I am working on representations of Kac-Moody Lie algebras. My PhD thesis is focused on Kostant-Kumar modules, which are certain cyclic submodules of the tensor product of two highest weight irreducible modules over a symmetrizable Kac-Moody Lie algebra.
Manika Gupta, K. N. Raghavan, Sankaran Viswanath, Kostant-Kumar modules: presentation and multiplicities- https://arxiv.org/abs/2608.14098
Kostant-Kumar modules are cyclic submodules of the tensor product of two highest weight irreducible modules over a symmetrizable Kac-Moody Lie algebra over an algebraically closed field of characteristic 0. A characterisation of the multiplicity of irreducibles is well known for the tensor product. We generalise this characterisation to Kostant-Kumar modules. We also give a generators and relations description of Kostant-Kumar modules in the finite dimensional and symmetric Kac-Moody algebra case. As an application of these results, we obtain Schur-positivity type results for symmetric functions corresponding to Kostant-Kumar modules. and obtain an upper bound for these refined multiplicities.
2. Symmetric and Alternating Square Multiplicity for Kostant Kumar Modules (in preparation with S. Viswanath)
Related to generators and relations of Kostant-Kumar modules and applications
Talk at CONTACT V Online Conference, March, 2026
Talk at Meru Combinatorics Conference, IIT Bhilai- June, 2026
Poster presentation at AlCoVE, online organised by University of Waterloo- June, 2026
Poster presentation at IMJ-PRG Summer School, Sorbonne University- June, 2026
Talk at PART I Online Conference, June, 2026
Talk at ICRA, online organised by Institut Fourier, Université Grenoble Alpes- July, 2026
Talk at ICECA, online organised by University of Haifa- Aug, 2026
Talk at International Combinatorics Conference, IISc, Bangalore- Aug, 2026