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Coinvariant algebras and fake degrees for spin Weyl groups of classical type

Published online by Cambridge University Press:  09 September 2013

CONSTANCE BALTERA  and
WEIQIANG WANG
CONSTANCE BALTERA
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA 22904, U.S.A. e-mails: cgb2k@virginia.edu, ww9c@virginia.edu
WEIQIANG WANG
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA 22904, U.S.A. e-mails: cgb2k@virginia.edu, ww9c@virginia.edu
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Abstract

The coinvariant algebra of a Weyl group plays a fundamental role in several areas of mathematics. The fake degrees are the graded multiplicities of the irreducible modules of a Weyl group in its coinvariant algebra, and they were computed by Steinberg, Lusztig and Beynon–Lusztig. In this paper we formulate a notion of spin coinvariant algebra for every Weyl group. Then we compute all the spin fake degrees for each classical Weyl group, which are by definition the graded multiplicities of the simple modules of a spin Weyl group in the spin coinvariant algebra. The spin fake degrees for the exceptional Weyl groups are given in a sequel.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 1 , January 2014 , pp. 43 - 79
Copyright
Copyright © Cambridge Philosophical Society 2013 

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