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Research

  • Jacobson-Morozov Lemma for Algebraic Supergroups, joint with V. Serganova. Submitted; Arxiv.

  • Semisimplification of the category of tilting modules for GL_n, joint with J. Brundan, P. Etingof, V. Ostrik. To appear in Advances in Mathematics; Arxiv.

  • Duflo-Serganova functor and a superdimension formula for the periplectic Lie superalgebra, joint with V. Serganova. Submitted; Arxiv.

  • Monoidal abelian envelopes and a conjecture of Benson--Etingof, joint with K. Coulembier, T. Heidersdorf. Submitted; Arxiv.

  • Kac-Wakimoto conjecture for the periplectic Lie superalgebra, joint with V. Serganova. To appear in Journal of Algebra and Applications; Arxiv.

  • Deligne categories and the periplectic Lie superalgebra, joint with V. Serganova. To appear in Moscow Math. Journal; Arxiv.

  • The affine VW supercategory, joint with M. Balagovic, Z. Daugherty, I. Halacheva, J. Hennig, M. S. Im, G. Letzter, E. Norton, V. Serganova, C. Stroppel. Sel. Math. New Ser. 26, 20 (2020); Arxiv.

  • Deligne categories and representations of the infinite symmetric group, joint with D. Barter, T. Heidersdorf.
    Advances in Mathematics, Vol. 346 (2019): 1-47; Arxiv.

  • Translation functors and decomposition numbers for the periplectic Lie superalgebra p(n), joint with M. Balagovic, Z. Daugherty, I. Halacheva, J. Hennig, M. S. Im, G. Letzter, E. Norton, V. Serganova, C. Stroppel.
    Mathematical Research Letters, Vol. 26 (2019), No. 3: 643-710; Arxiv.

  • Categorical actions on Deligne categories, Journal of Algebra 504 (2018): 391-431, Arxiv.

  • Deligne categories and the limit of categories Rep(GL(m|n)), joint with V. Serganova and V. Hinich. IMRN, 2020(15), 4602-4666; Arxiv.

  • Schur-Weyl duality for Deligne categories II: the limit case, Pacific Journal of Mathematics, Vol. 285 (2016), No. 1: 185-224; Arxiv.

  • Reduced Kronecker coefficients and Deligne categories, Journal of Algebraic Combinatorics, Volume 44 (2016), Issue 2: 345-362; Arxiv.

  • Schur-Weyl duality for Deligne categories, IMRN, vol. 18 (2015): 8959-9060; Arxiv.

  • On representations of rational Cherednik algebras of complex rank, Representation Theory 18, AMS (2014): 361-407; Arxiv.

    Notes:


  • Tables of action of translation functors on simples modules for the periplectic superalgebra.

  • Notes on restricted inverse limits of categories (short version included as appendix in Schur-Weyl duality for Deligne categories II: the limit case ). On the Arxiv.

  • Complex tensor power is a symmetric monoidal functor .

  • Notes and links from the MIT Seminar on Deligne categories (seminar homepage).