A (-q)-analogue of weight multiplicities
Author(s)Lusztig, George; Yun, Zhiwei
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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).
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of the Ramanujan Mathematical Society
Lusztig, George and Zhiwei Yun. “A (-q)-analogue of weight multiplicities.” Journal of the Ramanujan Mathematical Society 28A (2012)