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Title Truncated Weyl modules as Chari-Venkatesh modules and fusion products : Módulos de Weyl truncados via módulos de Chari-Venkatesh e produtos de fusão: Módulos de Weyl truncados via módulos de Chari-Venkatesh e produtos de fusão
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University/Publisher Universidade Estadual de Campinas
Abstract Abstract: We study structural properties of truncated Weyl modules. Given a simple Lie algebra g and a dominant integral weight \lambda, the graded local Weyl module W(\lambda) is the universal finite-dimensional graded highest-weight module for the current algebra g[t]= g\otimes C[t]. For each positive integer N, the quotient W_N(\lambda) of W(\lambda) by the submodule generated by the action of the ideal g\otimes t^NC[t] on the highest-weight vector is called a truncated Weyl module. It satisfies the same universal property as W(\lambda) when regarded as a module for the corresponding truncated current algebra g[t]_N=g \otimes \frac{C[t]}{t^NC[t]}. Chari-Fourier-Sagaki conjectured that if N\leq |\lambda|, W_N(\lambda) should be isomorphic to the fusion product of certain irreducible modules. Our main result proves this conjecture when \lambda is a multiple of a minuscule weight and g is simply laced. We also take a further step towards proving the conjecture for multiples of a ''small'' fundamental weight which is not minuscule by proving that the corresponding truncated Weyl module is isomorphic to the quotient of a fusion product of Kirillov-Reshetikhin modules by a very simple relation. One important part of the proof of our main result, and the second main result of this work, is a proof that any truncated Weyl module is isomorphic to a Chari-Venkatesh module and explicitly describes the corresponding family of partitions. This leads to further results in the case that g={sl}_2 related to Demazure flags and chains of inclusions of truncated Weyl modules
Subjects/Keywords Weyl, Módulos de; Produtos tensoriais; Representações de álgebras; Kac-Moody, Algebras de; Weyl modules; Tensor product; Representations of algebras; Kac-Moody algebras
Contributors UNIVERSIDADE ESTADUAL DE CAMPINAS (CRUESP); Moura, Adriano Adrega de, 1975- (advisor); Fourier, Ghislain (coadvisor); Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica (institution); Programa de Pós-Graduação em Matemática (nameofprogram); Kochloukov, Plamen Emilov (committee member); Matucci, Francesco (committee member); Guerreiro, Marines (committee member)
Language inglês
Country of Publication br
Record ID oai:repositorio.unicamp.br:REPOSIP/332339
Repository unicamp
Date Indexed 2020-09-09
Issued Date 2017-01-01 00:00:00
Note [] Orientador: Moura, Adriano Adrega de; [] Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica; [degreelevel] Doutorado; [degreediscipline] Matematica; [degreename] Doutor em Matemática; [sponsordocumentnumber] 140768/2016-5; [sponsor] CNPQ; [sponsor] CAPES;

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