Главная

Jonah Blasiak

  1. Representation theory of the nonstandard Hecke algebra.

    Чт, 01/12/2012 - 15:01 — SomNambul
    Authors: Jonah Blasiak
    Subjects: Representation Theory
    Abstract

    The nonstandard Hecke algebra \check{\mathscr{H}}_r was defined in GCT IV to
    study the Kronecker problem. We study a quotient \check{\mathscr{H}}_{r,2} of
    \check{\mathscr{H}}_r, called the nonstandard Temperley-Lieb algebra, which is
    simpler than \check{\mathscr{H}}_{r}. It is defined to be the subalgebra of
    H_{r,2} \otimes \mathscr{H}_{r,2} generated by \mathcal{P}_i := C'_i \otimes
    C'_i + C_i \otimes C_i, i \in [r-1], where \mathscr{H}_{r,2} is the
    Temperley-Lieb algebra and C'_i and C_i are Kazhdan-Lusztig basis elements.

  2. Cyclage, catabolism, and the affine Hecke algebra.

    Втр, 01/12/2010 - 16:01 — SomNambul
    Authors: Jonah Blasiak
    Subjects: Combinatorics
    Abstract

    We identify a subalgebra \pH_n of the extended affine Hecke algebra \eH_n of
    type A. The subalgebra \pH_n is a \u-analogue of the monoid algebra of \S_n
    \ltimes \ZZ_{\geq 0}^n and inherits a canonical basis from that of \eH_n. We
    show that its left cells are naturally labeled by tableaux filled with positive
    integer entries having distinct residues mod n, which we term \emph{positive
    affine tableaux} (PAT).

  3. An insertion algorithm for catabolizability.

    Пнд, 08/17/2009 - 18:30 — SomNambul
    Authors: Jonah Blasiak
    Subjects: Combinatorics
    Abstract

    Motivated by our recent work relating canonical bases to combinatorics of
    Garsia-Procesi modules \cite{B}, we give an insertion algorithm that computes
    the catabolizability of the insertion tableau of a standard word. This allows
    us to characterize catabolizability as the statistic on words invariant under
    Knuth transformations, certain (co)rotations, and a new operation called a
    catabolism transformation. We also prove a Greene's Theorem-like
    characterization of catabolizability, and a result about how cocyclage changes
    catabolizability, strengthening a similar result in \cite{SW}.

Math-arch

RSS-материал