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Combinatorics of the $\widehat {\frak sl}_2$ Coinvariants: Dual Functional Realization and Recursion

Published online by Cambridge University Press:  04 December 2007

B. Feigin ,
R. Kedem ,
S. Loktev ,
T. Miwa  and
E. Mukhin
B. Feigin
Affiliation:
Landau Institute for Theoretical Physics, Chernogolovka, 142432, Russia
R. Kedem
Affiliation:
Department of Mathematics University of Illinois, Urbana/Champaign, U.S.A.
S. Loktev
Affiliation:
Independent University of Moscow, B. Vlasievsky per, 11, Moscow, Russia
T. Miwa
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606, Japan. e-mail: tetsuji@kusm.kyoto-u.ac.jp
E. Mukhin
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A. e-mail: mukhin@math.iupui.edu
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Abstract

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We give the fermionic character formulas for the spaces of coinvariants obtained from level k integrable representations of $\widehat {\frak sl}_2$. We establish the functional realization of the spaces dual to the coinvariant spaces. We parameterize functions in the dual spaces by rigged partitions, and prove the recursion relations for the sets of rigged partitions.

Keywords

coinvariantsfermionic character formulas
Type
Research Article
Information
Compositio Mathematica , Volume 134 , Issue 2 , November 2002 , pp. 193 - 241
Copyright
© 2002 Kluwer Academic Publishers