Generalized exponents of small representations. II

Details Generalized exponents of small representations. II Generalized exponents of small representations. II

2009-04-16

arxiv.org/abs/0904.2487v1

Mathematics

Representation Theory

70 pg

Scientific paper

This is the second paper in a sequence devoted to giving manifestly non-negative formulas for generalized exponents of small representations in all types. It contains a first formula for generalized exponents of small weights which extends the Shapiro-Steinberg formula for classical exponents. The formula is made possible by a computation of Fourier coefficients of the degenerate Cherednik kernel. Unlike the usual partition function coefficients, the answer reflects only the combinatorics of minimal expressions as a sum of roots.

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