Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-09-18T12:08:32.765Z Has data issue: false hasContentIssue false
  • English
  • Français

The Spin Representation of the Symmetric Group

Published online by Cambridge University Press:  20 November 2018

A. O. Morris
A. O. Morris*
Affiliation:
University College of Wales, Aberystwyth, Wales
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Γn be the representation group or spin group (9; 4) of the symmetric group Sn. Then the irreducible representations of Γn can be allocated into two classes which we shall call (i) ordinary representations, which are the irreducible representations of the symmetric group, and (ii) spin or projective representations.

As is well known (3; 5), there is an ordinary irreducible representation [λ] corresponding to every partition (λ) = (λ1, λ2, . . . , λm) of n with

λ1 ≥ λ2 ≥ . . . ≥ λm > 0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 543 - 549
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Brauer, R. and Robinson, G. de B., On a conjecture by Nakayama, Trans. Roy. Soc. Can., Sec. I l l (3), 41 (1947), 11–19, 20-25.Google Scholar
2. Frame, J. S., Robinson, G. de B., and Thrall, R. M., The hook graphs of the symmetric group, Can. J. Math., 6 (1954), 316–324.Google Scholar
3. Littlewood, D. E., The theory of group characters and matrix representations of groups (Oxford, 1950).Google Scholar
4. Morris, A. O., The spin representation of the symmetric group, Proc. London Math. Soc. (3), 12 (1962), 55–76.Google Scholar
5. Morris, A. O., On Q-functions, J. London Math. Soc, 37 (1962), 445–455.Google Scholar
6. Nakayama, T., On some modular properties of irreducible representations of a symmetric group I, II,Japan. J. Math., 17 (1941), 165–184, 277-294.Google Scholar
7. de, G. Robinson, B., On the representations of the symmetric group III, Amer. J. Math., 70 (1948), 277–294.Google Scholar
8. de, G. Robinson, B., Representation theory of the symmetric group (Toronto, 1961).Google Scholar
9. Schur, I., Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitionen, J. Reine Angew. Math., 189 (1911), 155–250.Google Scholar