Generalized exponents of small representations. II

Ion, Bogdan

doi:10.1090/S1088-4165-2011-00372-1

Generalized exponents of small representations. II
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by Bogdan Ion

Represent. Theory 15 (2011), 433-493

DOI: https://doi.org/10.1090/S1088-4165-2011-00372-1

Published electronically: May 24, 2011

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Abstract:

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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