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Published online by Cambridge University Press:  05 January 2014

Tullio Ceccherini-Silberstein
Affiliation:
Università degli Studi del Sannio, Italy
Fabio Scarabotti
Affiliation:
Università degli Studi di Roma 'La Sapienza', Italy
Filippo Tolli
Affiliation:
Università degli Studi Roma Tre
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References

[1] H., Akazawa and H., Mizukawa, Orthogonal polynomials arising from the wreath products of a dihedral group with a symmetric group. J. Combin. Theory Ser.A 104 (2003), no. 2, 371–380.Google Scholar
[2] J.L., Alperin and R.B., Bell, Groups and Representations. Graduate Texts in Mathematics, vol. 162, Springer-Verlag, New York, 1995.
[3] R.A., Bailey, C.E., Praeger, C.A., Rowley and T.P., Speed, Generalized wreath products of permutation groups. Proc. London Math. Soc. (3) 47 (1983), no. 1, 69–82.Google Scholar
[4] E., Bannai and T., Ito, Algebraic Combinatorics, Benjamin, 1984.
[5] Ya.G., Berkovich and E.M., Zhmud, Characters of Finite Groups. Part 1. Translations of Mathematical Monographs, vol. 172, American Mathematical Society, 1998.
[6] Ya.G., Berkovich and E.M., Zhmud, Characters of Finite Groups. Part 2. Translated from the Russian manuscript by P., Shumyatsky, V., Zobina and Ya.G., Berkovich. Translations of Mathematical Monographs, vol. 181. American Mathematical Society, 1999.
[7] D., Bump, Lie Groups. Graduate Texts in Mathematics, vol. 225, Springer-Verlag, 2004.
[8] T., Ceccherini-Silberstein, Yu., Leonov, F., Scarabotti and F., Tolli, Generalized Kaloujnine groups, uniseriality and height of automorphisms. Internat. J. Algebra Comput. 15 (2005), no. 3, 503–527.Google Scholar
[9] T., Ceccherini-Silberstein, F., Scarabotti and F., Tolli, Trees, wreath products and finite Gelfand pairs. Adv. Math. 206 (2006), no. 2, 503–537.Google Scholar
[10] T., Ceccherini-Silberstein, F., Scarabotti and F., Tolli, Finite Gelfand pairs and applications to probability and statistics. J. Math. Sci. 141 (2007), no. 2, 1182–1229.Google Scholar
[11] T., Ceccherini-Silberstein, F., Scarabotti and F., Tolli, Harmonic Analysis on Finite Groups: Representation Theory, Gelfand Pairs and Markov Chains. Cambridge Studies in Advanced Mathematics, vol. 108, Cambridge University Press, 2008.
[12] T., Ceccherini-Silberstein, A., Machì, F., Scarabotti and F., Tolli, Induced representation and Mackey theory. J. Math. Sci. 156 (2009), no. 1, 11–28.Google Scholar
[13] T., Ceccherini-Silberstein, F., Scarabotti and F., Tolli, Clifford theory and applications. J. Math. Sci. 156 (2009), no. 1, 29–43.Google Scholar
[14] T., Ceccherini-Silberstein, F., Scarabotti and F., Tolli, Representation theory of wreath products of finite groups. J. Math. Sci. 156 (2009), no. 1, 44–55.Google Scholar
[15] T., Ceccherini-Silberstein, F., Scarabotti and F., Tolli, Representation Theory of the Symmetric Groups: the Okounkov-Vershik Approach, Character Formulas, and Partition Algebras. Cambridge Studies in Advanced Mathematics, vol. 121, Cambridge University Press, 2010.
[16] A.H., Clifford, Representations induced in an invariant subgroup. Ann. Math. (2) 38 (1937), no. 3, 533–550.Google Scholar
[17] C.W., Curtis and I., Reiner, Representation Theory of Finite Groups and Associative Algebras. Reprint of the 1962 original. Wiley Classics Library. John Wiley & Sons, 1988.
[18] C.W., Curtis and I., Reiner, Methods of Representation Theory. With Applications to Finite Groups and Orders, Vols. I and II. Pure and Applied Mathematics Series, John Wiley & Sons, 1981 and 1987.
[19] P., Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl. 10 (1973). Available at: http://users.wpi.edu/~martin/RESEARCH/philips.pdfGoogle Scholar
[20] P., Diaconis, Group Representations in Probability and Statistics. Institute of Mathematical Statistics Lecture Notes-Monograph Series, vol. 11, Institute of Mathematical Statistics, 1988.
[21] P., Diaconis and D., Rockmore, Efficient computation of isotypic projections for the symmetric group, in Proc. Conf. on Groups and computation (New Brunswick, NJ, 1991), pp. 87–104, American Mathematical Society, 1993.
[22] P., Diaconis and M., Shahshahani, Time to reach stationarity in the Bernoulli—Laplace diffusion model. SIAM J. Math. Anal. 18 (1987), 208–218.Google Scholar
[23] J.D., Dixon and B., Mortimer, Permutation groups. Graduate Texts in Mathematics, vol. 163, Springer-Verlag, 1996.
[24] L., Dornhoff, Group Representation theory. Part A: Ordinary Representation Theory. Pure and Applied Mathematics Series, 7, Marcel Dekker, 1971.
[25] C.F., Dunkl, A Krawtchouk polynomial addition theorem and wreath products of symmetric groups. Indiana Univ. Math. J. 25 (1976), 335–358.Google Scholar
[26] C.F., Dunkl, An addition theorem for Hahn polynomials: the spherical functions. SIAM J. Math. Anal. 9 (1978), 627–637.Google Scholar
[27] C.F., Dunkl, Orthogonal functions on some permutation groups. in Proc. Symp. Pure Math. vol. 34, pp. 129–147, American Mathematical Society, 1979.
[28] A., Figà-Talamanca, An application of Gelfand pairs to a problem of diffusion in compact ultrametric spaces, in Topics in Probability and Lie Groups: Boundary Theory, CRM Proc. Lecture Notes vol. 28, American Mathematical Society, 2001.
[29] W., Fulton and J., Harris, Representation Theory. A First Course. Graduate Texts in Mathematics, vol. 29, Springer-Verlag, 1991.
[30] P.X., Gallagher, Group characters and normal Hall subgroups. Nagoya Math. J. 21 (1962), 223–230.Google Scholar
[31] L., Geissinger and D., Kinch, Representations of the hyperoctahedral group, J. Algebra 53 (1978), 1–20.Google Scholar
[32] I.M., Gelfand, Spherical functions on symmetric Riemannian spaces, Dokl. Akad. Nauk. SSSR 70 (1959), 5–8 (Collected papers, Vol. II, Springer (1988), 31–35).Google Scholar
[33] R.I., Grigorchuk, Just infinite branch groups, in New Horizons in pro-p Groups, Progr. Math., vol. 184, pp. 121–179, Birkhäuser, 2000.
[34] L.C., Grove, Groups and Characters. Pure and Applied Mathematics John Wiley & Sons, Inc., 1997.
[35] B., Huppert, Character Theory of Finite Groups. De Gruyter Expositions in Mathematics, vol. 25, Walter de Gruyter, 1998.
[36] I.M., Isaacs, Character Theory of Finite Groups. Corrected reprint of the 1976 original (Academic Press, New York). Dover Publications, 1994.
[37] G.D., James, The Representation Theory of the Symmetric Groups. Springer Lecture Notes, vol. 682, Springer-Verlag, 1978.
[38] G.D., James and A., Kerber, The Representation Theory of the Symmetric Group. Encyclopedia of Mathematics and its Applications, vol. 16, Addison-Wesley, 1981.
[39] L., Kaloujnine, Sur les p-groupes de Sylow du groupe symétrique du degré pm. C. R. Acad. Sci. Paris 221 (1945), 222–224.Google Scholar
[40] L., Kaloujnine, Sur les p-groupes de Sylow du groupe symétrique du degré pm (Suite centrale ascendante et descendante). C. R. Acad. Sci. Paris 223 (1946), 703–705.Google Scholar
[41] L., Kaloujnine, Sur les p-groupes de Sylow du groupe symétrique du degré pm (Sous-groupes caractéristiques, sous-groupes parallélotopiques), C. R. Acad. Sci. Paris 224 (1947), 253–255.Google Scholar
[42] L., Kaloujnine, La structure des p-groupes de Sylow des groupes symétriques finis. Ann. Sci. École Norm. Sup. (3) 65 (1948), 239–276.Google Scholar
[43] A., Kerber, Representations of Permutation Groups. I. Lecture Notes in Mathematics, vol. 240, Springer-Verlag, 1971.
[44] A., Kerber, Applied Finite Group Actions. Second edition. Algorithms and Combinatorics Series, vol. 19, Springer-Verlag, 1999.
[45] A., Kerber and J., Tappe, On permutation characters of wreath products. Discrete Math. 15 (1976), no. 2, 151–161.Google Scholar
[46] M., Krasner and L., Kaloujnine, Produit complet des groupes de permutations et problème d'extension de groupes I. Acta Sci. Math. Szeged 13 (1950), 208–230.Google Scholar
[47] M., Krasner and L., Kaloujnine, Produit complet des groupes de permutations et problème d'extension de groupes II. Acta Sci. Math. Szeged 14 (1951), 39–66.Google Scholar
[48] M., Krasner and L., Kaloujnine, Produit complet des groupes de permutations et problème d'extension de groupes III. Acta Sci. Math. Szeged 14 (1951), 69–82.Google Scholar
[49] S., Lang, SL2(R). Reprint of the 1975 edition. Graduate Texts in Mathematics, vol. 105. Springer-Verlag, 1985.
[50] S., Lang, Algebra. Revised third edition. Graduate Texts in Mathematics, vol. 211, Springer-Verlag, 2002.
[51] G., Letac, Problèmes classiques de probabilité sur un couple de Gelfand, in “Analytical Problems in Probability”, Lecture Notes in Mathematics, vol. 861, pp. 93–120, Springer Verlag, 1981.
[52] G., Letac, Les fonctions spheriques d'un couple de Gelfand symmetrique et les chaînes de Markov. Advances Appl. Prob. 14 (1982), 272–294.Google Scholar
[53] W.C.W., Li, Number Theory with Applications. Series on University Mathematics, vol. 7, World Scientific, 1996.
[54] J.H. van, Lint and R.M., Wilson, A Course in Combinatorics. Second edition. Cambridge University Press, 2001.
[55] G.W., Mackey, Unitary representations of group extensions. I. Acta Math. 99 (1958), 265–311.Google Scholar
[56] G.W., Mackey, Unitary Group Representations in Physics, Probability, and Number Theory. Second edition. Advanced Book Classics, Addison-Wesley, 1989.
[57] H., Mizukawa, Zonal spherical functions on the complex reflection groups and (n + 1, m + 1)-hypergeometric functions, Adv. Math 184 (2004), 1–17.Google Scholar
[58] H., Mizukawa and H., Tanaka, (n + 1, m + 1)-hypergeometric functions associated to character algebras. Proc. Amer. Math. Soc. 132 (2004), no. 9, 2613–2618.
[59] A., Okounkov and A.M., Vershik, A new approach to representation theory of symmetric groups. SelectaMath. (N.S.) 2 (1996), no. 4, 581–605.Google Scholar
[60] J.J., Rotman, An Introduction to the Theory of Groups. Fourth edition. Graduate Texts in Mathematics, vol. 148, Springer-Verlag, 1995.
[61] B.E., Sagan, The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions. Second edition. Graduate Texts in Mathematics, 203, Springer-Verlag, 2001.
[62] J., Saxl, On multiplicity-free permutation representations, in Finite Geometries and Designs, London Mathematical Society Lecture Notes Series, vol. 48, p. 337–353, Cambridge University Press, 1981.
[63] F., Scarabotti and F., Tolli, Harmonic analysis of finite lamplighter random walks. J. Dyn. Control Syst. 14 (2008), no. 2, 251–282.Google Scholar
[64] F., Scarabotti and F., Tolli, Harmonic analysis on a finite homogeneous space. Proc. Lond. Math. Soc.(3) 100 (2010), no. 2, 348–376.Google Scholar
[65] F., Scarabotti and F., Tolli, Harmonic analysis on a finite homogeneous space II: the Gelfand-Tsetlin decomposition. Forum Math. 22 (2010), no. 5, 879–911.Google Scholar
[66] C.H., Schoolfield, A signed generalization of the Bernoulli–Laplace diffusion model. J. Theoret. Probab. 15 (2002), no. 1, 97–127.Google Scholar
[67] J.P., Serre, Linear representations of finite groups. Graduate Texts in Mathematics, vol. 42, Springer-Verlag, 1977.
[68] B., Simon, Representations of Finite and Compact Groups. American Mathematical Society, 1996.
[69] R.P., Stanley, Enumerative Combinatorics, vol. 1. Cambridge University Press, 1997.
[70] D., Stanton, Orthogonal Polynomials and Chevalley Groups, in Special Functions: Group Theoretical Aspects and Applications (R., Askeyet al., Eds.) pp. 87–128, Dordrecht, 1984.
[71] D., Stanton, Harmonics on Posets. J. Comb. Theory Ser.A 40 (1985), 136–149.Google Scholar
[72] D., Stanton, An introduction to group representations and orthogonal polynomials, in Orthogonal Polynomials (P., Nevai, Ed.), pp. 419–433, Kluwer Academic, 1990.
[73] S., Sternberg, Group Theory and Physics. Cambridge University Press, 1994.
[74] A., Terras, Fourier Analysis on Finite Groups and Applications. London Mathematical Society Student Texts, vol. 43, Cambridge University Press, 1999.
[75] H., Wielandt, Finite Permutation Groups. Academic Press, 1964.
[76] E., Wigner, On unitary representations of the inhomogeneous Lorentz group. Ann. Math. (2) 40 (1939), no. 1, 149–204.Google Scholar

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  • References
  • Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, Italy, Fabio Scarabotti, Università degli Studi di Roma 'La Sapienza', Italy, Filippo Tolli, Università degli Studi Roma Tre
  • Book: Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups
  • Online publication: 05 January 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107279087.005
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  • References
  • Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, Italy, Fabio Scarabotti, Università degli Studi di Roma 'La Sapienza', Italy, Filippo Tolli, Università degli Studi Roma Tre
  • Book: Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups
  • Online publication: 05 January 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107279087.005
Available formats
×

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  • References
  • Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, Italy, Fabio Scarabotti, Università degli Studi di Roma 'La Sapienza', Italy, Filippo Tolli, Università degli Studi Roma Tre
  • Book: Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups
  • Online publication: 05 January 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781107279087.005
Available formats
×