Generalized Schur algebras

Preprint English OPEN
Kleshchev, Alexander; Muth, Robert;
(2018)
  • Subject: Mathematics - Representation Theory

We define and study a new class of bialgebras, which generalize certain Turner double algebras related to generic blocks of symmetric groups. Bases and generators of these algebras are given. We investigate when the algebras are symmetric, which is relevant to block the... View more
  • References (9)

    [BK] J. Brundan and A. Kleshchev, Modular Littlewood-Richardson coefficients, Math. Z. 232 (1999), 287-320.

    [EK1] A. Evseev and A. Kleshchev, Turner doubles and generalized Schur algebras, Adv. Math. 317 (2017), 665-717.

    [EK2] A. Evseev and A. Kleshchev, Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality, Ann. of Math. (2), 188 (2018), no. 2, 453-512.

    [G] J.A. Green, Polynomial representations of GLn, 2nd edition, Springer-Verlag, Berlin, 2007.

    [KM] A. Kleshchev and R. Muth, Schrifying quasihereditary algebras, preprint, University of Oregon, 2018.

    [MZ] F. Marko and A.N. Zubkov, Schur superalgebras in characteristic p. II. Bull. London Math. Soc. 38(2006), 99-112.

    [T1] W. Turner, Rock blocks, Mem. Amer. Math. Soc. 202 (2009), no. 947.

    [T2] W. Turner, Tilting equivalences: from hereditary algebras to symmetric groups, J. Algebra 319 (2008), 3975-4007.

    [T3] W. Turner, Bialgebras and caterpillars, Q. J. Math. 59 (2008), 379-388.

  • Related Organizations (1)
    MSRI ( MSRI )
    United States
    90%
  • Metrics
Share - Bookmark