# 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} }

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…

## 5 Citations

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## References

SHOWING 1-10 OF 11 REFERENCES

### Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions

- Mathematics
- 2005

### Fusion Product Structure of Demazure Modules

- Mathematics
- 2013

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 ?

- Mathematics
- 2008

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

- Mathematics
- 2009

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

- Mathematics
- 2013

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

- Mathematics
- 2000

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

- Mathematics
- 1998

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…