## Research

I am interested in the representation theory of infinite-dimensional(Kac-Moody) Lie algebras and quantum groups, especially its intersection with algebraic combinatorics(Macdonald polynomials) and number theory (modular forms, mock-theta functions). More recently, I have been trying to use the theory of Macdonald polynomials to understand the characters of Demazure mdoules.

## Publications

**R. Biswal**, G. Fourier;*Minuscule Schubert Varieties: Poset Polytopes, PBW-degenerated Demazure Modules, and Kogan Faces*, Algebras and Representation Theory,**18**, (2015), Issue 6, pages 1481-1503.[arXiv:1410.1126]**R. Biswal**, V. Chari, L. Schneider, S. Viswanath;*Demazure Flags, Chebyshev Polynomials, Partial and Mock Theta functions*, Journal of Combinatorial Theory, Series A,**140**, (2016), pages 38-75. [arXiv:1502.05322]**R. Biswal**, V. Chari, D. Kus;*Demazure Flags, q-Fibonacci Polynomials and Hypergeometric Series*, Res. Math. Sci. 5 (2018), no. 1, Paper No. 12, 34 pp [arXiv:1607.01069]**R. Biswal**, D. Kus;*A combinatorial formula for graded multiplicities in excellent filtrations*, Transformation Groups, (2021), Vol. 26, pp. 81-114, [arXiv:1712.02667]**R. Biswal**, T. Scrimshaw;*Existence of Kirillov Reshetikhin crystals for multiplicity free nodes*, Publ. Res. Inst. Math. Sci., (2020), Volume 56, 761-778, [arXiv:1901.00182]**R. Biswal**, V. Chari, P. Shereen, J. Wand;*Macdonald polynomials and level two Demazure modules for affine sl_{n+1}*, Journal of Algebra, Volume 575, (2021), pages 159-191. [arXiv:1910.05848]- G. Benkart,
**R. Biswal**, E.Kirkmann, V. Nguyen, J. Zhu;*Mckay matrices for finite dimensional Hopf algebras*, Canad. J. Math. (2021), pp. 1–46. [arXiv:2007.05510] - G. Benkart,
**R. Biswal**, E.Kirkmann, V. Nguyen, J. Zhu;*Tensor representations for the Drinfeld double of the Taft algebras,*(To appear in Journal of Algebra)[arXiv:2012.15277] **R. Biswal**, T. Scrimshaw;*Kirillov Reshetikhin crystals B^{7,s} for type E_7^1*(To appear in Communications in Algebra).[arXiv:1901.00182]**R. Biswal**, A. Chakhar, X. He;*Classification of rank two Lie conformal algebras*(To appear in Journal of Ramanujan Mathematical Society).[arXiv:1712.02667]

## Papers Submitted/In Preparation

**R. Biswal**, Susan J. Sierra;*Ideals in enveloping algebras of affine Kac-Moody algebras,*(submitted, 34 pages)[ arXiv:2112.08334 ]