Survey Articles

I am honored to be have co-authored the following articles in tribute to Georgia Benkart:

1.  T. Halverson and  A. Ram, Gems from the work of Georgia Benkart. Notices Amer. Math. Soc. 69 (2022), no. 3, 375–384.

2.  A. Adem, T. Halverson, A. Ram, E. Zelmanov, Remembering Georgia Benkart. Notices Amer. Math. Soc. 70 (2023), no. 3, 420–433

Recent Talks

1.  Great Permutations (video), Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart, Simons Laufer Mathematical Sciences Institution (SLMath), May 3, 2024.

Publications

1.   T. Halverson and A. Ram, Monk Rules for Type GLn Macdonald Polynomials, Journal of Algebra, 655 (2024), 493-516, special issue of Journal of Algebra dedicated to the memory of Georgia Benkart. [journal]  [arXiv]. 

2.  E. Chen*, J. DeJong*, T. Halverson, D. Shuman, Signal Processing on the Permutahedron: Tight Spectral Frames for Ranked Data Analysis, Journal of Fourier Analysis and Applications, 27 (2021), 70 pp. [Journal] [arXiv]

3.   S. Armon* and T. Halverson, Transition matrices between Young’s natural and seminormal representations, Electronic Journal of Combinatorics, 28 (3) (2021). [Journal] [arXiv]

4.   T. Halverson and T.N. Jacobson*, Set-partition tableaux and representations of diagram algebras, Algebraic Combinatorics, 3 (2020) p. 509-538. [Journal] [arXiv]

5.   G. Benkart and T. Halverson, Partition Algebras and the Invariant Theory of the Symmetric Group. Recent Trends in Algebraic Combinatorics, Springer International Publishers, Association for Women in Mathematics, 16 (2019). [Journal] [arXiv]

6.   G. Benkart and T. Halverson, Partition algebras P_k(n) with 2k>n and the fundamental theorems of invariant theory for the symmetric group Sn, Journal of the London Mathematical Society (2) 99 (2019), 194-224. [Journal] [arXiv]

7.   G. Benkart, T. Halverson, and N. Harman, Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups, Journal of Algebraic Combinatorics, 46 (2017), 77-108. [Journal] [arXiv]

8.   J. Barnes*, G. Benkart, and T. Halverson, McKay Centralizer Algebras, Proceedings of the London Mathematical Society, (3) 112 (2016), no. 2, 375-414. [Journal] [arXiv]

9.   C. Topaz, L. Ziegelmeier, and T. Halverson, Topological Data Analysis of Biological Aggregation Models, PLoS ONE 10(5): e0126383. [Journal] [arXiv]

10.   T. Halverson and M. Reeks*, Gelfand Models for Diagram Algebras, Journal of Algebraic Combinatorics, 41 (2015), 229-255. [Journal] [arXiv]

11.   G. Benkart and T. Halverson, Motzkin Algebras, European Journal of Combinatorics, 36 (2014), 473-502. [Journal] [arXiv]

12.   E. delMas* and T. Halverson, Representations of the Rook-Brauer Algebra, Communications in Algebra, 42 (2013), 423-443. [Journal] [arXiv]

13.   T. Halverson and N. Thiem, q partition algebra combinatorics, J. Combinatorial Theory Series A, 117 (2010), 507-527. [Journal] [arXiv]

14.   T. Halverson, M. Mazzocco, and A. Ram, Commuting families in Hecke and Temperley-Lieb algebras, Nagoya Math J, 195 (2009), 125-152. [Journal] [arXiv]

15.   D. Flath, T. Halverson, and K. Herbig*, The planar rook algebra and Pascal’s triangle, L’Enseignement Mathematique (2), 55 (2009), 77-92. [Journal] [arXiv]

16.   T. Halverson and A. Ram, Partition algebras, European J. Combinatorics, 26 (2005), 869-921. [Journal] [arXiv]

17.   T. Halverson and T. Lewandowski*, RSK insertion for set partitions and diagram algebras, Electronic J. Combinatorics, 11, (2004/6) Research Paper 24, 24 pp (electronic). [Journal] [arXiv]

18.   T. Halverson, Representations of the q-rook monoid, J. Algebra, 273 (2004), 227-251. [Journal]

19.   J. Farina* and T. Halverson, Character orthogonality for the partition algebra and fixed points of permutations, Advances in Applied Math, 31 (2003), 113-131. [Journal]

20.   M. Dieng*, T. Halverson, and V. Poladian*, Character formulas for q-rook monoid algebras, Journal of Algebraic Combinatorics, 17 (2003), 99-123. [journal]

21.   A. Cantrell*, T. Halverson, and B. Miller*, Robinson-Schensted-Knuth insertion and characters of cyclotomic Hecke algebras, Journal of Combinatorial Theory Series A, 99 (2002), 17-31. [journal]

22.   T. Halverson and A. Ram, q-rook monoid algebras, Hecke algebras, and Schur-Weyl duality, Zapiski Nauchanyh Seminarov POMI, 283 (2001), 224-250 and Journal of Mathematical Sciences, 121 No. 3 (2004), 2419-2439. [journal] [arXiv]

23.   T. Halverson, Characters of the partition algebras, Journal of Algebra, 238, (2001), 502-533. [journal]

24.   T. Halverson and A. Ram, Bitraces for GL_n(F_q) and the Iwahori-Hecke algebra of type A_{n-1}, Indagationes Mathhematicae (N.S.) 10 (1999) 247-268. [journal]

25.   T. Halverson and A. Ram, Murnaghan-Nakayama rules for characters of Iwahori-Hecke algebras of complex reflection groups G(r,p,n), Canadian Journal of Mathematics, 50 (1998), 167-192. [journal] [arXiv]

26.   T. Halverson, R. Leduc, and A. Ram, Iwahori-Hecke algebras of type A, bitraces and symmetric functions, International Mathematics Research Notices, (1997), 401-416. [journal [Paper]

27. T. Halverson, Characters of the centralizer algebra of mixed tensor representations of GL(r,C) and the quantum group Uq(gl(r,C)), Pacific Journal of Mathematics, 174 (1996), 359-410. [journal]

28.   T. Halverson and A. Ram, Murnaghan-Nakayama rules for characters of Iwahori-Hecke algebras of classical type, Transactions of the American Mathematical Society, (1996), 3967-3995. [journal]

29.   T. Halverson and A. Ram, Characters of algebras containing a Jones basic construction: the Temperley-Lieb, Okada, Brauer, and Birman-Wenzl algebras, Advances in Mathematics, 116 (1995), 263-321. [journal]

30.   T. Halverson, A q-rational Murnaghan-Nakayama rule, Journal of Combinatorial Theory Series A, (1995), 1-18. [journal]

31.   G. Benkart, M. Chakrabarti, T. Halverson, R. Leduc, C. Lee, and J. Stroomer, Tensor product representations of general linear groups and their connections with Brauer algebras, Journal of Algebra 166 (1994), 529-567. [journal]

Conference Proceedings

1. 1. 1.   T. Halverson, Set Partition Tableaux, Symmetric Group Multiplicities, and Partition algebra Modules, Proceedings of the 31st Conference on Formal Power Series and Algebraic Combianatorics (FPSAC 2019), Ljubljana, Slovenia. 

      2.   G. Benkart and T. Halverson, McKay Centralizer Algebras, Proceedings of the 28th Conference on Formal Power Series and Algebraic Combianatorics (FPSAC 2016), Vancouver, Canada.

      3.   T. Halverson, Gelfand Models for Diagram Algebras, Proceedings of the 27th Conference on Formal Power Series and Algebraic Combianatorics (FPSAC 2015), Paris, France.