Demazure Modules, Fusion Products and Q-Systems

Chari, Vyjayanthi; Venkatesh, R.

doi:10.1007/s00220-014-2175-x

Cited by 45 publications

(130 citation statements)

References 34 publications

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“…We begin this section by briefly reminding the reader of the definition of a Demazure module occurring in a highest weight integrable irreducible representation of the affine Lie algebra sl 2 . We are interested only in stable Demazure modules and we recall several results from [6] about this family. We end the section by proving Proposition 2.3.…”

Section: Demazure Modules and The Proof Of Proposition 23mentioning

confidence: 99%

Demazure flags, Chebyshev polynomials, partial and mock theta functions

Biswal

Chari

Schneider

et al. 2016

Journal of Combinatorial Theory, Series A

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Abstract.We study the level m-Demazure flag of a level ℓ-Demazure module for sl2 [t]. We define the generating series A ℓ→m n (x, q) which encodes the q-multiplicity of the level m Demazure module of weight n. We establish two recursive formulae for these functions. We show that the specialization to q = 1 is a rational function involving the Chebyshev polynomials. We give a closed form for A ℓ→ℓ+1 n (x, q) and prove that it is given by a rational function. In the case when m = ℓ + 1 and ℓ = 1, 2, we relate the generating series to partial theta series. We also study the specializations A 1→3 n (q k , q) and relate them to the fifth order mock-theta functions of Ramanujan.

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Section: Demazure Modules and The Proof Of Proposition 23mentioning

confidence: 99%

Demazure flags, Chebyshev polynomials, partial and mock theta functions

Biswal

Chari

Schneider

et al. 2016

Journal of Combinatorial Theory, Series A

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“…where the exponent indicates the number of times that part is repeated. Together with results from [1,11,10], Theorem 2.4.1 leads to further results in the case that g = sl 2 related to Demazure flags and chains of inclusions of truncated Weyl modules. For instance, from the description of ξ λ N and results from [11], one can immediately identify the truncated Weyl modules which are isomorphic to Demazure modules.…”

Section: Introductionmentioning

confidence: 54%

“…Together with results from [1,11,10], Theorem 2.4.1 leads to further results in the case that g = sl 2 related to Demazure flags and chains of inclusions of truncated Weyl modules. For instance, from the description of ξ λ N and results from [11], one can immediately identify the truncated Weyl modules which are isomorphic to Demazure modules. Otherwise, the results of [1,10] allows us to study Demazure flags for truncated Weyl modules since every CV module (for g = sl 2 ) admits a Demazure flag.…”

Section: Introductionmentioning

confidence: 54%

On truncated Weyl modules

Fourier

Martins

Moura

2019

Communications in Algebra

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We study structural properties of truncated Weyl modules. A truncated Weyl module WN (λ) is a local Weyl module for g [t], where g is a finite-dimensional simple Lie algebra. It has been conjectured that, if N is sufficiently small with respect to λ, the truncated Weyl module is isomorphic to a fusion product of certain irreducible modules. Our main result proves this conjecture when λ is a multiple of certain fundamental weights, including all minuscule ones for simply laced g. We also take a further step towards proving the conjecture for all multiples of fundamental weights by proving that the corresponding truncated Weyl module is isomorphic to a natural quotient of a fusion product of Kirillov-Reshetikhin modules. One important part of the proof of the main result shows 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 = sl2 related to Demazure flags and chains of inclusions of truncated Weyl modules.Part of this work was developed while the second author was a visiting Ph.D. student at the University of Cologne. He thanks Peter Littelmann and Deniz Kus for their guidance and support during that period and the University of Cologne for hospitality. He also thanks CAPES and CNPq (SWE 203324/2014-5) for the financial support.A. M. was partially supported by CNPq grant 304477/2014-1 and Fapesp grant 2014/09310-5.

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“…Our first result constructs a large family (which includes the Demazure modules) of finite-dimensional modules for Cg which admit a Demazure flag. Analogous results for A (1) 1 were established in [6] using results from [7]. In the current situation, we use results from [14]; however, we have to work much harder to establish the analogous results of [6] for two reasons.…”

Section: Introductionmentioning

confidence: 91%

Demazure flags, q-Fibonacci polynomials and hypergeometric series

2018

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We study a family of finite-dimensional representations of the hyperspecial parabolic subalgebra of the twisted affine Lie algebra of type A (2) 2 . We prove that these modules admit a decreasing filtration whose sections are isomorphic to stable Demazure modules in an integrable highest weight module of sufficiently large level. In particular, we show that any stable level m Demazure module admits a filtration by level m Demazure modules for all m ≥ m . We define the graded and weighted generating functions which encode the multiplicity of a given Demazure module and establish a recursive formulae. In the case when m = 1, 2 and m = 2, 3, we determine these generating functions completely and show that they define hypergeometric series and that they are related to the q-Fibonacci polynomials defined by Carlitz.

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Demazure Modules, Fusion Products and Q-Systems

Cited by 45 publications

References 34 publications

Demazure flags, Chebyshev polynomials, partial and mock theta functions

Demazure flags, Chebyshev polynomials, partial and mock theta functions

On truncated Weyl modules

Demazure flags, q-Fibonacci polynomials and hypergeometric series

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