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.

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), to appear in *Sém. Lothar. Combin.*.

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

The Hopf structure of symmetric group
characters as symmetric functions
(with M. Zabrocki) preprint (2018).