Demazure Modules, Chari{Venkatesh Modules and Fusion Products ?

@article{Ravinder2014DemazureMC,
  title={Demazure Modules, Chari\{Venkatesh Modules and Fusion Products ?},
  author={B. Ravinder},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2014},
  volume={10},
  pages={110}
}
  • B. Ravinder
  • Published 1 September 2014
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
Let g be a finite-dimensional complex simple Lie algebra with highest root . Given two non-negative integers m, n, we prove that the fusion product of m copies of the level one Demazure module D(1; ) with n copies of the adjoint representation ev0V ( ) is independent of the parameters and we give explicit defining relations. As a consequence, for g simply laced, we show that the fusion product of a special family of Chari{Venkatesh modules is again a Chari{Venkatesh module. We also get a… 

Simplified presentations and embeddings of Demazure modules

For an untwisted affine Lie algebra we prove an embedding of any higher level Demazure module into a tensor product of lower level Demazure modules (e.g. level one in type A) which becomes in the

Fusion products and toroidal algebras

We study the category of finite--dimensional bi--graded representations of toroidal current algebras associated to finite--dimensional complex simple Lie algebras. Using the theory of graded

On truncated Weyl modules

Abstract We study structural properties of truncated Weyl modules. A truncated Weyl module is a local Weyl module for , where is a finite-dimensional simple Lie algebra. It has been conjectured that,

DEMAZURE MODULES OF LEVEL TWO AND PRIME REPRESENTATIONS OF QUANTUM AFFINE $\mathfrak{sl}_{n+1}$

We study the classical limit of a family of irreducible representations of the quantum affine algebra associated to $\mathfrak{sl}_{n+1}$ . After a suitable twist, the limit is a module for

References

SHOWING 1-10 OF 11 REFERENCES

Fusion Product Structure of Demazure Modules

Let 𝔤 be a finite–dimensional complex simple Lie algebra. Given a non–negative integer ℓ, we define 𝓟ℓ+$\mathcal {P}^{+}_{\ell }$ to be the set of dominant weights λ of 𝔤 such that ℓΛ0+λ is a

The PBW Filtration, Demazure Modules and Toroidal Current Algebras ?

Let L be the basic (level one vacuum) representation of the affine Kac-Moody Lie algebra b. The m-th space Fm of the PBW filtration on L is a linear span of vectors of the form x1 ···xlv0, where l m,

A categorical approach to Weyl modules

Global and local Weyl modules were introduced via generators and relations in the context of affine Lie algebras in [CP2] and were motivated by representations of quantum affine algebras. In [FL] a

Demazure Modules, Fusion Products and Q-Systems

In this paper, we introduce a family of indecomposable finite-dimensional graded modules for the current algebra associated to a simple Lie algebra. These modules are indexed by an

Weyl modules for classical and quantum affine algebras

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible

On generalized Kostka polynomials and quantum Verlinde rule

Here we propose a way to construct generalized Kostka polynomials. Namely, we construct an equivariant filtration on tensor products of irreducible representations. Further, we discuss properties of

The arithmetic theory of loop algebras

Weyl modules, Demazure modules and finite crystals for non-simply laced type