Representations of Lie superalgebras with Fusion Flags

Kus, Deniz

doi:10.1093/imrn/rnx058

Cited by 4 publications

(5 citation statements)

References 29 publications

(53 reference statements)

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“…In [BCM19], the authors extended the definition of local Weyl modules to map superalgebras g ⊗ C A with g being any finite-dimensional simple Lie superalgebra nonisomorphic to q(n), and fit these local Weyl modules into a categorical framework similar to the one in [CFK10]. In [FM17] and [Kus18], the authors focused in the study of local Weyl modules for the current superalgebra osp(1|2) [t]. In [FM17], the authors computed the dimension and characters of such modules and related them to non-symmetric Macdonald polynomials; and in [Kus18], the author realized local Weyl modules as certain fusion products, provided generators and relations for fusion products, studied Demazure-type and truncated Weyl modules.…”

Section: Introductionmentioning

confidence: 99%

“…In [FM17] and [Kus18], the authors focused in the study of local Weyl modules for the current superalgebra osp(1|2) [t]. In [FM17], the authors computed the dimension and characters of such modules and related them to non-symmetric Macdonald polynomials; and in [Kus18], the author realized local Weyl modules as certain fusion products, provided generators and relations for fusion products, studied Demazure-type and truncated Weyl modules.…”

Section: Introductionmentioning

confidence: 99%

“…One should notice that fusion products are also used in [FM17,Kus18], as well as an important tool used in [CL06,FL07,Nao12] to prove Chari and Pressley's conjecture. These modules were first defined in [FL99, Definition 1.7] to be graded versions of tensor products of evaluation modules evaluated at different points of C (known as fusion parameters).…”

Section: Introductionmentioning

confidence: 99%

“…Demazure-type modules. In[Kus18], D. Kus defined analogues of Demazure modules for the Lie superalgebra osp(1|2)[t], and called them Demazure-type modules. In this subsection, we give a similar definition for the Lie superalgebra sl(1|2)[t].…”

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confidence: 99%

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Local Weyl modules and fusion products for the current superalgebra $\mathfrak{sl}(1|2)[t]$

Brito¹,

Calixto²,

Macedo³

2019

Preprint

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We study a class modules, called Chari-Venkatesh modules, for the current superalgebra sl(1|2) [t]. This class contains other important modules, such as graded local Weyl, truncated local Weyl and Demazure-type modules. We prove that Chari-Venkatesh modules can be realized as fusion products of generalized Kac modules. In particular, this proves Feigin and Loktev's conjecture, that fusion products are independent of their fusion parameters, in the case where the fusion factors are generalized Kac modules. As an application of our results, we obtain bases, dimension and character formulas for Chari-Venkatesh modules.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Local Weyl modules and fusion products for the current superalgebra $\mathfrak{sl}(1|2)[t]$

Brito¹,

Calixto²,

Macedo³

2019

Preprint

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“…In [CLS], Calixto, Lemay and Savage initiated the study of Weyl modules for Lie superalgebras by defining local and global Weyl modules for map superalgebras of the form g ⊗ C A, where g is either a finite-dimensional basic classical Lie superalgebra, or sl(n, n) with n ≥ 2, and A is an associative, commutative algebra with unit, both defined over C. Weyl modules for Lie superalgebras also appear in [FM] and [Kus17].…”

Section: Introductionmentioning

confidence: 99%

Weyl Modules and Weyl Functors for Lie Superalgebras

Bagci

Calixto

Macedo

2018

Algebr Represent Theor

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Given an algebraically closed field k of characteristic zero, a Lie superalgebra g over k and an associative, commutative k-algebra A with unit, a Lie superalgebra of the form g ⊗ k A is known as a map superalgebra. Map superalgebras generalize important classes of Lie superalgebras, such as, loop superalgebras (where A = k[t, t −1 ]), and current superalgebras (where A = k[t]). In this paper, we define Weyl functors, global and local Weyl modules for all map superalgebras where g is either sl(n, n) with n ≥ 2, or a finite-dimensional simple Lie superalgebra not of type q(n). Under certain conditions on the triangular decomposition of these Lie superalgebras we prove that global and local Weyl modules satisfy certain universal and tensor product decomposition properties. We also give necessary and sufficient conditions for local (resp. global) Weyl modules to be finite dimensional (resp. finitely generated).2010 Mathematics Subject Classification. 17B65, 17B10.

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Weyl Modules for Toroidal Lie Algebras

Mukherjee

Pattanayak²,

Sharma³

2022

Algebr Represent Theor

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In this paper, we extend the notion of Weyl modules for twisted toroidal Lie algebra T (µ). We prove that the level one global Weyl modules of T (µ) are isomorphic to the tensor product of the level one representation of twisted affine Lie algebras and certain lattice vertex algebras. As a byproduct, we calculate the graded character of the level one local Weyl modules of T (µ).Notations:• The sets of complex numbers, integers, non-negative integers, and positive integers are denoted by C, Z, Z ≥0 , and Z >0 , respectively.and the sets Z n , Z n ≥0 , and Z n >0 are defined similarly. • For n ≥ 2, we denote the elements (m 1 , . . . , m n ) ∈ Z n and (m 2 , . . . , m n ) ∈ Z n−1 by m and m, respectively. • Let A n := C[t ±1 1 , t ±1 2 , . . . , t ±1 n ] be the set of Laurent polynomial ring in n variables. • For m = (m 1 , . . . , m n ) ∈ Z n and m = (m 2 , . . . , m n ) ∈ Z n−1 the notation t m and t m represents t m 1 1 • • • t mn n and t m 2 2 • • • t mn n , respectively, in A n . • Let U(g) denotes the universal enveloping algebra of g and L n (g) denotes the Lie algebra g ⊗ A n with commutator given by [x ⊗ t m , y ⊗ t n ] = [x, y] ⊗ t m+n .

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Representations of Lie superalgebras with Fusion Flags

Cited by 4 publications

References 29 publications

Local Weyl modules and fusion products for the current superalgebra $\mathfrak{sl}(1|2)[t]$

Local Weyl modules and fusion products for the current superalgebra $\mathfrak{sl}(1|2)[t]$

Weyl Modules and Weyl Functors for Lie Superalgebras

Weyl Modules for Toroidal Lie Algebras

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