Rekha Biswal

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

  1. 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]
  2. 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]
  3. 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]
  4. R. Biswal, D. Kus; A combinatorial formula for graded multiplicities in excellent filtrations, Transformation Groups, (2021), Vol. 26, pp. 81-114, [arXiv:1712.02667]
  5. 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]
  6. 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]
  7. 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]

Papers Submitted/In Preparation

  1. R. Biswal, A. Chakhar, X. He; Classification of rank two Lie conformal algebras (submitted, 23 pages).[arXiv:1712.02667]
  2. R. Biswal, T. Scrimshaw; Kirillov Reshetikhin crystals B^{7,s} for type E_7^1 (submitted, 13 pages).[arXiv:1901.00182]
  3. G. Benkart, R. Biswal , E.Kirkmann, V. Nguyen, J. Zhu; Tensor representations for the Drinfeld double of the the Taft algebras, (submitted, 39 pages)[arXiv:2012.15277]