# Journal of the Ramanujan Mathematical Society

Volume 28A, Issue SPL, July – Special Issue 2013 pp. 311–340.

A (-q)-analogue of weight multiplicities**Authors**: George Lusztig and Zhiwei Yun

**Author institution:**Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139

**Summary:**We prove a conjecture in [L11] stating that certain polynomials Pσy,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 G can be expressed in terms of these polynomials Pσy,w (q).

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