Research

Current PhD Students

Alison Becker
Adam Buck
Will Erickson
Alex Heaton

Graduated PhD Students

Hassan Lhou (2016)
Wayne Andrew Johnson (2015)
Lauren Kelly Williams (2013)
Pamela Estephania Harris (2012)
Anthony van Groningen (2007)

Current Research

Joint with Hassan Lhou (UW-Milwaukee)
Lowest sl(2)-types in sl(n)-representations.
Represent. Theory
21 (2017), 20–34. PDF


Joint with Roger Howe (Yale) and Markus Hunziker (Baylor)
Symmetry: Representation Theory and its Applications Progress in Mathematics, 257. Birkhäuser/Springer, New York, 2014. xxviii+538 pp.
ISBN: 978-1-4939-1589-7; 978-1-4939-1590-3 00B30
CLICK HERE


Joint with Anthony van Groningen (MSOE)
The cubic, the quartic, and the exceptional group G_2 PDF
Developments and retrospectives in Lie theory, 385–397, Dev. Math., 38, Springer, Cham, 2014.


Joint with Pamela E. Harris (currently West Point, previous Marquette University)
Sums of squares of the Littlewood-Richardson coefficients and GL(n)-harmonic polynomials. PDF
Symmetry: representation theory and its applications, 305–326, Progr. Math., 257, Birkhäuser/Springer, New York, 2014.


Joint with Michael W. Hero (University of Iowa, previous UW-Milwaukee) and Lauren Kelly Williams (Mercyhurst University, previous UW-Milwaukee)
The measurement of quantum entanglement and enumeration of graph coverings. PDF
American Mathematics Society Contemporary Mathematics Series


Joint with Roger Howe (Yale), Steven Jackson (UMass-Boston), Soo Teck Lee (NUS) and Eng-Chye Tan (NUS)
Toric Degeneration of Branching Algebras PDF
Advances in Mathematics. 220 (2009), no. 6, 1809–1841.


Joint with Michael W. Hero (University of Iowa, former UW-Milwaukee)
Stable Hilbert series as related to the measurement of quantum entanglement PDF
Discrete Math. 309 (2009), no. 23-24, 6508-6514.


Joint with Jay H. Beder (UW-Milwaukee)
Invariance of generalized wordlength patterns. PDF
J. Statist. Plann. Inference 139 (2009), no. 8, 2706-2714.


Stable Hilbert series of S(g)^K for classical groups.
PDF
Journal of Algebra  314 (2007), no. 2, 844–871.


Joint with Ian M. Musson (UW-Milwaukee)
Invariant Differential Operators and FCR factors of Enveloping algebras. PDF
Communications in Algebra 36  (2008),  no. 10, 3759–3777.


Joint with Gregg Zuckerman (YALE)

  • Small semisimple subalgebras of semisimple Lie algebras. PDFHarmonic analysis, group representations, automorphic forms and invariant theory, 403–429, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 12, World Sci. Publ., Hackensack, NJ, 2007.
  • A generating function for Blattner’s formula. PDF
    Proceedings of the American Mathematical Society 136 (2008), no. 6, 2261–2270.

Joint with Roger Howe (YALE) and Eng-Chye Tan (National University of Singapore)

  • Stable Branching Rules for Classical Symmetric Pairs. PDF
    Transactions of the AMS.
  • Reciprocity Algebras and Branching for Classical Symmetric Pairs. PDF
    To Appear in the proceedings for the conference in honor of Hermann Weyl.
  • A Basis for the GLn Tensor Product Algebra. PDF
    Advances in Mathematics.
  • The Stability of Graded Multiplicity in the Setting of the Kostant-Rallis Theorem.
    PDF
    Transform. Groups 13 (2008), no. 3-4, 617–636.

Joint with Thomas Enright (UCSD):


An Application of the Littlewood Restriction Formula to the Kostant–Rallis Theorem. PDF
Transactions of the AMS.


A stable range for dimensions of homogeneous O(n)-invariant polynomials on the n x n matrices. PDF
Journal of Algebra.


Joint with Nolan R. Wallach (UCSD).
On Some q-Analogs of a Theorem of Kostant-Rallis. PDF
Canadian Journal of Mathematics.