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.
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), Advances in Applied Math. Volume 95, April 2018, Pages 96–115.
Products of characters of the symmetric group
(with M. Zabrocki) Journal of Combinatorial Theory, Series A,
165, (2019), pages 299-324.
Commutation and normal ordering for operators on symmetric functions
(with E. Briand, P. McNamara
and M. Rosas), Sém. Lothar. Combin. 80 (2019), Article B80d.
An insertion algorithm on multiset
partitions with applications to diagram algebras (with L. Colmenarejo,
F. Saliola, A. Schilling and M. Zabrocki)
Journal of Algebra, 557 (2020), 97128.
A combinatorial model for the
decomposition of multivariate polynomials rings as an $S_n$-module
(with M. Zabrocki) The Elect. Journal of Comb.
27(3) (2020), #P3.24.
The Hopf structure of symmetric group
characters as symmetric functions (with M. Zabrocki)
Symmetric group characters as symmetric functions
(with M. Zabrocki)
Paper No. 107943, 34 pp.
Plethysm and the algebra of
uniform block permutations (with F. Saliola, A. Schilling and M. Zabrocki)
The mystery of plethysm coefficients
(with L. Colmenarejo, F. Saliola, A. Schilling and M. Zabrocki)
preprint (2022).
Howe duality of the symmetric group
and a multiset partition algebra (with M. Zabrocki)
51 (2023), no. 1, 393–413.
Marked Graphs and the Chromatic
Symmetric Function (with J. Aliste-Prieto, A. De Mier and J. Zamora)
accepted in SIAM J. Discrete Math (SIDMA) (2023).
The symmetric group through
a dual perspective (with M. Zabrocki) to appear in Notices of AMS (2023).
