Canonical bases of higher-level q-deformed Fock spaces and Kazhdan-Lusztig polynomials
نویسنده
چکیده
The aim of this paper is to generalize several aspects of the recent work of LeclercThibon and Varagnolo-Vasserot on the canonical bases of the level 1 q-deformed Fock spaces due to Hayashi. Namely, we define canonical bases for the higher-level qdeformed Fock spaces of Jimbo-Misra-Miwa-Okado and establish a relation between these bases and (parabolic) Kazhdan-Lusztig polynomials for the affine Weyl group of type A (1) r−1. As an application we derive an inversion formula for a sub-family of these polynomials. ∗Research Institute for Mathematical Sciences, Kyoto University, 606 Kyoto, Japan.
منابع مشابه
Canonical bases of higher-level q-deformed Fock spaces
We define canonical bases of the higher-level q-deformed Fock space modules of the affine Lie algebra sl n generalizing the result of Leclerc and Thibon for the case of level 1. We express the transition matrices between the canonical bases and the natural bases of the Fock spaces in terms of certain affine Kazhdan-Lusztig polynomials. Leclerc and Thibon defined, in [6], a canonical basis of th...
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تاریخ انتشار 1999