Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A study of Kostant-Kumar modules via Littelmann paths   We study, by means of Littelmann's theory of paths, Kostant-Kumar modules (KK
modules for short), which by definition are certain submodules of the tensor
product of two irreducible integrable highest weight representations of a
symmetrizable Kac-Moody algebra. Our main result is an identification of a path
model for any KK module as a subset of the well known path model for the tensor
product consisting of concatenations of Lakshmibai-Seshadri paths. The
technical results about extremal elements in Coxeter groups that we formulate
and prove en route and the technique of their proofs should be of independent
interest. We also discuss the existence of PRV components and generalised PRV
components in KK modules.
  Specialising to the case of the special linear Lie algebra, we record a
decomposition rule for KK modules in terms of Littlewood-Richardson tableaux.
In this connection, we present a new procedure to determine the permutation
that is the initial element of the minimal standard lift of a semi-standard
Young tableau. The appendix, necessitated by the derivation of the tableau
decomposition rule, deals with standard concatenations of Lakshmibai-Seshadri
paths of arbitrary shapes, of which semi-standard Young tableaux form a very
special case.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics