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My research is in the Representation Theory of reductive Lie groups and related algebraic structures, such as affine Hecke algebras. Most problems that I work on are motivated by abstract harmonic analysis questions, like the study of unitary representations as part of the more general framework of the local Langlands program. This work has been supported by research grants from the EPSRC (2016-20, 2021-22), NSF-DMS and NSA-AMS (prior to 2015).

Preprints (arXiv)

  1. Some unipotent Arthur packets for reductive p-adic groups, with L. Mason-Brown and E. Okada, arXiv 2021, 51 pages. 

  2. A nonabelian Fourier transform for tempered unipotent representations, with A.-M. Aubert and B. Romano, arXiv 2021, 52 pages.

  3. Deformations of unitary Howe dual pairs, with H. De Bie, M. De Martino, R. Oste, arXiv:2009.05412, 26 pages.

  4. The nonabelian Fourier transform for elliptic unipotent representations of exceptional p-adic groups, arXiv:2006.13540v2, 27 pages.

  5. Symplectic Dirac operators for Lie algebras and graded Hecke algebras, with M. De Martino and P. Meyer, arXiv:2003.11279, 26 pages, to appear in Transformation Groups.

  6. Hermitian forms for affine Hecke algebras, with D. Barbasch, arXiv, 30 pages.

 

Publications

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  1. Weyl groups, the Dirac inequality, and isolated unitary unramified representations, Indag. Math. (special issue in the memory of T.A. Springer) 2022, vol 33, issue 1, 1-23.

  2. Cocenters of p-adic groups, III: elliptic and rigid cocenters, with X. He, Peking Math. J. (2021), vol 4, issue 2, 159-186.

  3. Dirac induction for rational Cherednik algebras, with M. De Martino, IMRN 17 (2020), 5155-5214.

  4. The Dunkl-Cherednik deformation of a Howe duality, with M. De Martino, J. Algebra 560 (2020), 914-959.

  5. Star operations for graded affine Hecke algebras, with D. Barbasch, Representation Theory, Automorphic Forms & Complex Geometry (A Tribute to Wilfried Schmid), International Press Boston, 2020, 107-138.

  6. On the reducibility of induced representations for classical p-adic groups and related affine Hecke algebras, with V. Heiermann, Israel J. Math. 231 (2019), no. 1, 379-417.

  7. An Euler-Poincare formula for a depth zero Bernstein projector, with D. Barbasch and A. Moy, Represent. Theory 23 (2019), 154-187.

  8. Types and unitary representations of reductive p-adic groups, Invent. Math. 213 (2018) no. 1, 237-269.

  9. One-W-type modules for rational Cherednik algebras and two-sided cells,  Bull. Inst. Math. Acad. Sin. (N.S.), 13 (2018) no. 1, 1-29.

  10. On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups, with E. Opdam, 18 pages, to appear in "Representation Theory, Number Theory, and Invariant Theory: In Honor of Roger Howe on the Occasion of His 70th Birthday", Progr. Math., Birkhauser.

  11. A uniform classification of discrete series representations of affine Hecke algebras, with E. Opdam,  Algebra and Number Theory 11 (2017), no.5, 1089-1134.

  12. One-W-type modules for rational Cherednik algebras and two-sided cells, arxiv, 29 pages, to appear in Bull. Inst. Math. Acad. Sin. (N.S.), volume in honor of George Lusztig on his 70th birthday.

  13. Dirac cohomology for symplectic reflection algebras,  Selecta Math 22 (2016), no. 1, 111-144.

  14. Cocenters and representations of affine Hecke algebras, with X. He, Jour. Eur. Math. Soc. 19 (2017), 3143-3177.

  15. Ladder representations of GL(n,Q_p), with D. Barbasch, "Representations of Reductive Groups: In Honor of David A Vogan, Jr. on his 60th Birthday”, Birkhauser, Progr. Math. 312 (2016), 117-137.

  16. The cocenter of the graded affine Hecke algebra and the density theorem, with X. He,  J. Pure Appl. Algebra 220 (2016), no. 1, 382-410. 

  17. Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index, with X He,  Adv. Math. 283 (2015), 1-50.

  18. Formal degrees of unipotent discrete series representations and the exotic Fourier transform, with E. Opdam,  Proc. London Math. Soc. 110 (2015), no. 3, 615-646. 

  19. Dirac cohomology of one-W-type representations, with A. Moy, Proc. Amer. Math. Soc. 143 (2015), no. 3, 1001-1013.

  20. Unitary Hecke algebra modules with nonzero Dirac cohomology, with D. Barbasch, Symmetry in Representation Theory and Its Applications: In honor of Nolan Wallach, Progr. Math. Birkhauser 257 (2015), 1-21.

  21. Special unipotent representations, with P. Trapa, in appendix to Small representations, string instantons, and Fourier modes of Eisenstein series by M. B. Green, S. D. Miller, and P. Vanhove, J. Number Theory 146 (2015), 252-257.

  22. Algebraic and analytic Dirac induction for graded affine Hecke algebras, with E. Opdam and P. Trapa, J. Inst. Math. Jussieu 13 (2014), no. 3, 447-486.

  23. Unitary equivalences for reductive p-adic groups, with D. Barbasch,  Amer. J. Math. 135 (2013), no. 6, 1633-1674.

  24. Characters of Springer representations on elliptic conjugacy classes, with P. Trapa,  Duke Math. J. 162 (2013), no. 2, 201-223.

  25. Dirac cohomology for graded affine Hecke algebras, with D. Barbasch and P. Trapa,  Acta Math. 209 (2012), no. 2, 197-227. 

  26. On characters and formal degrees of discrete series of affine Hecke algebras of classical types, with M. Kato and S. Kato,  Invent. Math. 187 (2012), 589-635.

  27. Spin representations of Weyl groups and the Springer correspondence, J. Reine Angew. Math. 671 (2012), 199-222.

  28. Duality between GL(n,R) and the degenerate affine Hecke algebra for gl(n), with P. Trapa, Amer. J. Math. 134 (2012), 141-170. 

  29. Regular orbits of symmetric subgroups on partial flag varieties, with K. Nishiyama and P. Trapa, Representation Theory, Complex Analysis, and Integral Geometry, Birkhauser (2012), 61-86.

  30. Reducibility of generic unipotent standard modules, with D. Barbasch,  J. Lie Theory 21 (2011), 837-846.

  31. Ramanujan bigraphs associated with SU(3) over a p-adic field, with C. Ballantine,  Proc. Amer. Math. Soc. 139 (2011), 1939-1953. 

  32. Tempered modules in exotic Deligne-Langlands classification, with S. Kato, Adv. Math.  226 (2011), 1538-1590.

  33. Functors for unitary representations of real classical groups and affine Hecke algebras, with P. Trapa, Adv. Math. 227 (2011), 1585-1611.

  34. Whittaker generic unitary dual for affine graded Hecke algebras of type E, with D. Barbasch, Compositio Math. 145 (2009), 1563-1616.

  35. On unitary unipotent representations of p-adic groups and affine Hecke algebras with unequal parameters, Represent. Theory 12 (2008), 453-498. 

  36. Unitarizable minimal principal series of reductive groups, with D. Barbasch and A. Pantano, in Representation theory of real reductive Lie groups (in honor of W. Casselman and D. Milicic), Contemp. Math. 472, Amer. Math. Soc. (2008), 63-136.

  37. Multiplicity matrices for the affine graded Hecke algebra, J. Algebra 320 (2008), 3950-3983.

  38. Unitary I-spherical representations for the split p-adic E6, Represent. Theory 10 (2006), 435-480.

  39. Spherical unitary principal series, with D. Barbasch, Pure Appl. Math. Q. 1 (2005), volume in memory of A. Borel, 755-789.

  40. The unitary I-spherical dual for the split p-adic group of type F4,  Represent. Theory 9 (2005), 94-137

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