arXiv subjects

B. Ravinder

Publications and source records attributed to B. Ravinder.

5 recordsLinked to original sources

arXiv2018

Stability of the Chari-Loktev bases for local Weyl modules of $\mathfrak{sl}_{r+1}[t]$

We prove stability of the Chari-Loktev bases with respect to the inclusions of local Weyl modules of the current algebra $\mathfrak{sl}_{r+1}[t]$. This is conjectured in \cite{RRV2} and the $r=1$ case is proved in \cite{RRV1}. Local Weyl modules being known to be Demazure submodules in the level one representations of the affine Lie algebra $\widehat{\mathfrak{sl}_{r+1}}$, we obtain, by passage to the direct limit, bases for the level one representations themselves.

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arXiv2018

Bases for local Weyl modules in type $C$

We give a Poincare-Birkhoff-Witt type basis for local Weyl modules of the current algebra of type $C$. As a consequence, we get a fermionic character formula for these modules.

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arXiv2017

On Chari-Loktev bases for local Weyl modules in type $A$

This paper is a study of the bases introduced by Chari-Loktev for local Weyl modules of the current algebra associated to a special linear Lie algebra. Partition overlaid patterns, POPs for short---whose introduction is one of the aims of this paper---form convenient parametrizing sets of these bases. They play a role analogous to that played by (Gelfand-Tsetlin) patterns in the representation theory of the special linear Lie algebra. The notion of a POP leads naturally to the notion of area of a pattern. We observe that there is a unique pattern of maximal area among all those with a given bounding sequence and given weight. We give a combinatorial proof of this and discuss its representation theoretic relevance. We then state a conjecture about the "stability", i.e., compatibility in the long range, of Chari-Loktev bases with respect to inclusions of local Weyl modules. In order to state the conjecture, we establish a certain bijection between colored partitions and POPs, which may be of interest in itself.

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arXiv2017

Generalized Demazure modules and fusion products

Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra with highest root $θ$ and let $\mathfrak{g}[t]$ be the corresponding current algebra. In this paper, we consider the $\mathfrak{g}[t]$-stable Demazure modules associated to integrable highest weight representations of the affine Lie algebra $\widehat{\mathfrak{g}}$. We prove that the fusion product of Demazure modules of a given level with a single Demazure module of a different level and with highest weight a multiple of $θ$ is a generalized Demazure module, and also give defining relations. This also shows that the fusion product of such Demazure modules is independent of the chosen parameters. As a consequence we obtain generators and relations for certain types of generalized Demazure modules. We also establish a connection with the modules defined by Chari and Venkatesh.

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arXiv2015

Stability of the Chari-Pressley-Loktev bases for local Weyl modules of $sl_2[t]$

We prove stability of the Chari-Pressley-Loktev bases for natural inclusions of local Weyl modules of the current algebra $sl_2[t]$. These modules being known to be Demazure submodules in the level 1 representations of the affine Lie algebra $\widehat{sl_2}$, we obtain, by passage to the direct limit, bases for the level 1 representations themselves.

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