Structure of coinvariants of affine $sl_2$ integrable modules

Rinat Kedem

University of Massachusetts, Amherst

May 5,
4:15pm
refreshments at 3:45pm
2-338

ABSTRACT 

We construct the space of coinvariants corresponding to the space of all possible compositions of $N$ intertwiners of integrable $\widehat{sl}_2$ modules with fixed level. We obtain an explicit basis for this space, as vectors in the integrable module itself. The construction leads to recursion relations for the characters of these spaces, resulting from a bijection with the space of (specially graded) Verlinde paths. The fermionic character formulas which result from the dual space description are finite analogs of those obtained by Feigin and Stoyanovsky. These imply some highly nontrivial statements about the dimensionality of certain spaces of symmetric polynomials.


Speaker's Contact Info: rinat(at-sign)math.umass.edu


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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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