Nonsymmetric RogersRamanujan sums and thick Demazure modules
Abstract
We consider expansions of products of thetafunctions associated with arbitrary root systems in terms of nonsymmetric Macdonald polynomials at $t=\infty$ divided by their norms. The latter are identified with the graded characters of Demazure slices, some canonical quotients of thick (upper) levelone Demazure modules, directly related to recent theory of generalized (nonsymmetric) global Weyl modules. The symmetric RogersRamanujantype series considered by CherednikFeigin were expected to have some interpretation of this kind; the nonsymmetric setting appeared necessary to achieve this. As an application, the coefficients of the nonsymmetric RogersRamanujan series provide formulas for the multiplicities of the expansions of tensor products of levelone KacMoody representations in terms of Demazure slices.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 DOI:
 10.48550/arXiv.1802.03819
 arXiv:
 arXiv:1802.03819
 Bibcode:
 2018arXiv180203819C
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Quantum Algebra