A (-q)-analogue of weight multiplicities
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1203.0521.pdf
Description
Submitted version
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296.95 KB
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Author(s)
Lusztig, George
Yun, Zhiwei
Date Issued
July 2013
Journal
Journal of the Ramanujan Mathematical Society
Citation
Lusztig, George and Zhiwei Yun. “A (-q)-analogue of weight multiplicities.” Journal of the Ramanujan Mathematical Society 28 (July 2013): 311-340.
Version
Original manuscript
Abstract
We prove a conjecture in [L11] stating that certain polynomials P-Y(sigma),(w)(q) introduced in [LV11] for twisted involutions in an affine Weyl group give ( -q)-analogues of weight multiplicities of the Langlands dual group G. We also prove that the signature of a naturally defined hermitian form on each irreducible representation of e can be expressed in terms of these polynomials P-Y(sigma),(w)(q).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://www.mathjournals.org/jrms/2013-028-000/2013-28A-SPL-014.html
