Fock Spaces for the q-Dunkl Kernel
نویسندگان
چکیده
منابع مشابه
(sl2) via Restricted q-Fock Spaces
Two restricted C[q, q]−forms of the well known q-boson algebra are introduced and the corresponding restricted q-Fock spaces defined. All of the irreducible highest weight representations, including the infinite dimensional ones, of U res ǫ (sl2) of type 1 are constructed through the restricted q-Fock spaces.
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A b s t r a c t . In [S], [KMS] the semi-infinite wedge construction of level 1 Uq(A (1)) Fock spaces and their decomposition into the tensor product of an irreducible Uq(A(1))-module and a bosonic Fock space were given. Here a general scheme for the wedge construction of q-deformed Fock spaces using the theory of perfect crystals is presented. Let Uq(fJ) be a quantum affine algebra. Let V be a...
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This paper studies the asymptotic behavior of the integral kernel of the Dunkl transform, the so-called Dunkl kernel, when one of its arguments is fixed and the other tends to infinity either within a Weyl chamber of the associated reflection group, or within a suitable complex domain. The obtained results are based on the asymptotic analysis of an associated system of ordinary differential equ...
متن کاملCanonical 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...
متن کاملLevel - 0 action of U q ( c sl n ) on the q - deformed Fock spaces
On the level-1 Fock space modules of the algebra U q ( b sl n ) we de ne a level-0 action U 0 of the U 0 q ( b sl n ), and an action of an Abelian algebra of conserved Hamiltonians commuting with the U 0 . An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials. 1 e-...
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ژورنال
عنوان ژورنال: Advances in Pure Mathematics
سال: 2012
ISSN: 2160-0368,2160-0384
DOI: 10.4236/apm.2012.23023