Representations of the Quantum Toroidal Algebra on Highest Weight Modules of the Quantum Affine Algebra of Type Gl[subscript N] PDF Download
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Author: Kouichi Takemura Publisher: ISBN: Category : Affine algebraic groups Languages : en Pages : 35
Book Description
Abstract: "A representation of the quantum toroidal algebra of type sl[subscript N] is constructed on every integrable irreducible highest weight module of the the [sic] quantum affine algebra of type gl[subscript N]. The q-version of the level-rank duality giving the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U[́subscript q](ĝl[subscript N]) of level L and U[́subscript q](ŝl[subscript L) of level N is described."
Author: Kouichi Takemura Publisher: ISBN: Category : Affine algebraic groups Languages : en Pages : 35
Book Description
Abstract: "A representation of the quantum toroidal algebra of type sl[subscript N] is constructed on every integrable irreducible highest weight module of the the [sic] quantum affine algebra of type gl[subscript N]. The q-version of the level-rank duality giving the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U[́subscript q](ĝl[subscript N]) of level L and U[́subscript q](ŝl[subscript L) of level N is described."
Author: Yoshihisa Saito Publisher: ISBN: Category : Affine algebraic groups Languages : en Pages : 28
Book Description
Abstract: "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[́subscript q](sl[subscript n, tor]) (n [> or =] 3) with the level (0,1). The quantum toroidal action on the Fock space depends on a certain parameter k. 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 U[subscript q](sl︠[︡subscript n]). Similarly, by a specific choice of the parameter, the level (1,0) vertex representation of the quantum toroidal algebra gives rise to a U[́subscript q](sl[subscript n, tor])- module structure on irreducible level-1 highest weight U[subscript q](sl︠[︡subscript n])-modules."
Author: Omar Foda Publisher: ISBN: Category : Quantum field theory Languages : en Pages : 43
Book Description
Abstract: "We discuss a construction of highest weight modules for the recently defined elliptic algebra A[subscript q, p] (ŝl2), and make several conjectures concerning them. The modules are generated by the action of the components of the operator L on the highest weight vectors. We introduce the vertex operators [phi] and [psi] through their commutation relations with the L-operator. We present ordering rules for the L- and [phi]-operators and find an upper bound for the number of linearly independent vectors generated by them, which agrees with the known characters of ŝl2 modules."
Author: Philipp Fleig Publisher: Cambridge Studies in Advanced ISBN: 1107189926 Category : Mathematics Languages : en Pages : 587
Book Description
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author: Publisher: American Mathematical Soc. ISBN: 0821838482 Category : Mathematics Languages : en Pages : 698
Book Description
Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.
Author: Adam Nyman Publisher: American Mathematical Soc. ISBN: 9780821865170 Category : Mathematics Languages : en Pages : 162
Book Description
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizataions, a significant class of examples in non-commutative algebraic geometry. More precisely, if $S$ is an affine, noetherian scheme, $X$ is a separated, noetherian $S$-scheme, $\mathcal{E}$ is a coherent ${\mathcal{O}}_{X}$-bimodule and $\mathcal{I} \subset T(\mathcal{E})$ is a graded ideal then we develop a compatibility theory on adjoint squares in order to construct the functor $\Gamma_{n}$ of flat families of truncated $T(\mathcal{E})/\mathcal{I}$-point modules of length $n+1$. For $n \geq 1$ we represent $\Gamma_{n}$ as a closed subscheme of ${\mathbb{P}}_{X^{2}}({\mathcal{E}}^{\otimes n})$. The representing scheme is defined in terms of both ${\mathcal{I}}_{n}$ and the bimodule Segre embedding, which we construct. Truncating a truncated family of point modules of length $i+1$ by taking its first $i$ components defines a morphism $\Gamma_{i} \rightarrow \Gamma_{i-1}$ which makes the set $\{\Gamma_{n}\}$ an inverse system. In order for the point modules of $T(\mathcal{E})/\mathcal{I}$ to be parameterizable by a scheme, this system must be eventually constant. In [20], we give sufficient conditions for this system to be constant and show that these conditions are satisfied when ${\mathsf{Proj}} T(\mathcal{E})/\mathcal{I}$ is a quantum ruled surface. In this case, we show the point modules over $T(\mathcal{E})/\mathcal{I}$ are parameterized by the closed points of ${\mathbb{P}}_{X^{2}}(\mathcal{E})$.
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Author: Kouichi Takemura![Representations of the Quantum Toroidal Algebra on Highest Weight Modules of the Quantum Affine Algebra of Type Gl[subscript N] PDF](https://books.google.com/books/content/images/frontcover/_b3EHAAACAAJ?fife=w80-h100)
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