RIMS-1133 TOROIDAL ACTIONS ON LEVEL 1 MODULES OF Uq ( ̂ sln).
نویسندگان
چکیده
We propose a proof of the recent observation due to Varagnolo and Vasserot that the q-deformed Fock spaces are modules of the quantum toroidal algebra U ′ q(sln,tor) (n ≥ 3) with the level (0, 1). The quantum toroidal action on the Fock space depends on a certain parameter κ. We find that with a specific choice of this parameter the action on the Fock spaces gives rise to the toroidal action on irreducible level-1 highest weight modules of the affine quantum algebra Uq(ŝln). Similarly, by a specific choice of the parameter, the level (1, 0) vertex representation of the quantum toroidal algebra gives rise to a U ′ q(sln,tor)-module structure on irreducible level-1 highest weight Uq(ŝln)-modules.
منابع مشابه
Toroidal and Level 0 U
(1) Utilizing a Braid group action on a completion of Uq(ŝln+1), an algebra homomorphism from the toroidal algebra Uq(sln+1,tor) (n ≥ 2) with fixed parameter to a completion of Uq(ĝln+1) is obtained. (2) The toroidal actions by Saito induces a level 0 U ′ q(ŝln+1) action on level 1 integrable highest weight modules of Uq(ŝln+1). Another level 0 U ′ q(ŝln+1) action is defined by Jimbo, et al., i...
متن کامل2 Yoshihisa Saito , Kouichi Takemura and Denis Uglov A
Recently Varagnolo and Vasserot established that the q-deformed Fock spaces due to Hayashi, and Kashiwara, Miwa and Stern, admit actions of the quantum toroidal algebra U ′ q(sln,tor) (n ≥ 3) with the level (0, 1). In the present article we propose a more detailed proof of this fact then the one given by Varagnolo and Vasserot. The proof is based on certain non-trivial properties of Cherednik’s...
متن کاملQuantum Toroidal Algebras and Their Vertex Representations
We construct the vertex representations of the quantum toroidal algebras Uq(sln+1,tor). In the classical case the vertex representations are not irreducible. However in the quantum case they are irreducible. For n=1, we construct a set of finitely many generators of Uq(sl2,tor).
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A Diagrammatic Category for the Representation Theory of Uq(sln) by Scott Edward Morrison Doctor of Philosophy in Mathematics University of California, Berkeley Professor Vaughan Jones, Chair This thesis provides a partial answer to a question posed by Greg Kuperberg in [24] and again by Justin Roberts as problem 12.18 in Problems on invariants of knots and 3-manifolds [28], essentially: Canwe ...
متن کاملTOROIDAL ACTIONS ON LEVEL 1 MODULES OF U q ( b sl n ) :
Recently Varagnolo and Vasserot established that the q-deformed Fock spaces due to Hayashi, and Kashiwara, Miwa and Stern, admit actions of the quantum toroidal algebra U 0 q (sl n;tor ) (n 3) with the level (0; 1). In the present article we propose a more detailed proof of this fact then the one given by Varagnolo and Vasserot. The proof is based on certain non-trivial properties of Cherednik'...
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