Professor of Mathematics

"My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful." -- Hermann Weyl.

Publications and Preprints


   The Hecke algebra of type B at roots of unity, Markov traces and subfactors. Ph.D. Thesis, UCSD 1999.

   Weights of Markov traces on Hecke algebras, J. Reine Angew Math. 508, (1999) 157-178.

   Markov traces and Hecke algebras at roots of unity, Proceedings of the Formal Power Series and Algebraic
        Combinatorics, 1999. pp. 405-416.

   Hecke algebras of type B and type D and Subfactors, Pacific Journal of Math.  Vol 199, No. 1 (2001)
       137-161.

   q-Centralizer algebras for spin groups (with H. Wenzl), Journal of Algebra, 253 (2002) 237-275.

   Rooted trees and the representation theory of iterated wreath products of abelian groups (with M.
        Orrison and D. Rockmore), Adv. in Applied Math. 33, Issue 3, (2004), 531-547.

    On the algebraic decomposition of centralizer algebras of the hyperoctahedral group, Contemporary
        Math. 376, (2005), 345-357.

    On the Kronecker product $s_{(n-p,p)}\ast s_{\lambda}$ (with C. Ballantine), Elec. Journal of
        Combinatorics. Vol. 12, (2005), #R28, 1-26.

    New Results on the Peak algebra (with M. Aguiar and K. Nyman), J. of Algebraic Combinatorics.
        Vol. 23, No.2 (2006), pg. 149-188

   Affine Braids, Markov traces and the category O, (with A. Ram) Algebraic groups and homogeneous
        spaces, 423-473, Tata Inst. Fund. Res. Stud. Math., Tata Inst. Fund. Res., Mumbai, 2007.

   A combinatorial interpretation for the coefficients in the Kronecker product s_{(n,n-p)}* s_\lambda
        (with C. Ballantine), Sém. Lothar. Combin. 54A (2006), Art. B54Af, 29 pp.

   On the partition algebras of complex reflection groups, Journal of Algebra, 313 (2007) 590-616.

   The Hopf Algebra of Uniform block Permutations (with M. Aguiar), J. Algebraic Combin. 28
       (2008), no. 1, 115--138.

       An extended abstract of 13 pages appeared in: Proceedings of the Formal Power Series and Algebraic
        Combinatorics 2005
Available at: http://lanl.arxiv.org/abs/math.RA/0505199.

   Cyclotomic Solomon Algebras (with A. Mathas), Adv. Math. 219 (2008), no. 2, 450--487.

   The Hilbert series for the ring of Hook Schur functions (with M. Zabrocki), Preprint.  

   Reduced Kronecker coefficients and counter-examples to Mulmuley's saturation conjecture SH, with an
       appendix by Ketan Mulmuley (with E. Briand and M. Rosas), Computational Complexity 18 (2009),
        no. 4, 577-600

   Quasipolynomial formulas for the Kronecker coefficients indexed by two two-row shapes (with E.
        Briand and M. Rosas), FPSAC 2009, Hagenberg, Austria, Discrete Mathematics and Theoretical
       Computer Science Proc.
AK, 2009, 241-252

    The stability of the Kronecker product of Schur functions (with E. Briand and M. Rosas) J. Algebra
        331 (2011), 11-27.

   The stability of the Kronecker product of Schur functions (with E. Briand and M. Rosas), Discrete
        Math. Theor. Comput. Sci. Proc.
, AN, pp. 557-567, Nancy, 2010.

   The partition algebra and the Kronecker product (with C. Bowman and M. De Visscher), Discrete
        Math. Theor. Comput. Sci. proc.
AS 2013, 321 - 332.

    The quasi-partition algebra (with Z. Daugherty), Journal of Algebra, Volume 404, 15 February 2014,
        Pages 124-151.

    Graphs with equal chromatic symmetric function (with G. Scott), Discrete Mathematics, Volume 320,
        6 April 2014, Pages 1-14

    Schur positivity in a square (with C. Ballantine), The Elect. Journal of Comb. 21 (3) (2014), #P3.46

   The partition algebra and the Kronecker coefficients (with C. Bowman and M. De Visscher),
        Trans. Amer. Math. Soc. 367 (2015), no. 5, 3647–3667.

   Rectangular symmetries for coefficients of symmetric functions (with E. Briand and M. Rosas),
        Elect. Journal of Comb., vol. 22, (3), (2015), #P3-15.

   Commutation and normal ordering for operators on symmetric functions (with E. Briand, P. McNamara
        and M. Rosas), preprint (2015).

   Symmetric group characters as symmetric functions (with M. Zabrocki) preprint (2016).

   The number of permutations with the same peak set for sign permutations (with F. Castro-Velez, A. Diaz-
       Lopez, J. Pastrana and R. Zevallos), Journal of Combinatorics, Vol. 8 , No. 4 (2017), pp. 631-652.

   A minimaj-preserving crystal on ordered multiset partitions (with G. Benkart, L. Colmenarejo, P. Harris,
        G. Panova, A. Schilling, and M. Yip), preprint (2017).