**Research**

Here are my preprints, publications,
lecture
notes, slides, conferences,
students,
and miscellanea.

The material below is based upon work partially supported by NSF
grants DMS-0071606, DMS-0300106,
DMS-0554118, DMS-0968275,
DMS-0968060, and DMS-1302237, NSA Grant
MSFP-06Y-095, and the Simons Foundation.

**Preprints:**

**A note on the orbits of a symmetric subgroup in the flag variety**

(with Leticia Barchini), February 2024,
preprint, arxiv

** Relating real and p-adic Kazhdan-Lusztig polynomials**

(with Leticia Barchini), February 2024,
preprint, arxiv

**Publications:**

**Unitary representations of real reductive groups**

(with Jeffrey Adams, Marc van Leeuwen, and David Vogan)
arxiv

*Astérisque*, volume 417 (2020), 186pp. Sample

**Reducible characteristic cycles of Harish Chandra modules for U(p,q) and the
Kashiwara-Saito singularity**

(with Leticia Barchini and Petr Somberg),
arxiv

*Communications in Algebra*,
Volume 47 (2019), no. 12, 4874-4888.

**Dirac index and twisted characters**

(with Dan Barbasch and Pavle Pandzic)
arxiv

*Transactions of the AMS*,
Volume 371 (2019), no. 3, 1701-1733.

**Laplacians on Spheres**

(with Henrik Schlichtkrull and David Vogan),
arxiv

*São Paulo Journal of Mathematics*,
Volume 12 (2018), no. 2, 295-358.

**Codimension one connectedness of the graph of associated varieties**

(with Kyo Nishiyama and Akihito Wachi)
arxiv

*Tohuku Journal of Math. (2)*,
Volume 68, Number 2 (2016), 199-239.

**The mathematical work of David A. Vogan, Jr.**

(with W. M. McGovern)
pdf

Representations of Reductive Groups (in Honor of the 60th
Birthday of David A. Vogan, Jr.),

Progress in Mathematics, volume 312 Birkhauser/Springer (2016), 1-10.

**Algebraic and analytic Dirac induction for graded affine Hecke algebras**

(with Dan Ciubotaru and Eric Opdam) arxiv or
final pdf

*Journal de l'Institute de Mathematiques de Jussieu (JIMJ)*,
**13** (2014), no. 3, 447-486.

**Appendix
to: Small
representations, string instantons, and Fourier modes of Eisenstein
series
by Michael B. Green, Stephen D. Miller, and Pierre Vanhove**

(with Dan Ciubotaru)
arxiv

*Journal of Number Theory*, **146** (2013), 187-309.

**Characters of Springer representations on elliptic conjugacy classes**

(with Dan Ciubotaru)
arxiv or
final pdf

*Duke Mathematical Journal*, **162** (2013), no. 2, 201-223.

**
Dirac cohomology for graded affine Hecke algebras
**

(with Dan Barbasch and Dan Ciubotaru)
arxiv
or
final pdf

*Acta Mathematica,* **209** (2012), no. 2, 197-227.

**The exotic Robinson-Schensted correspondence**

(with Anthony Henderson) arxiv

*Journal of Algebra*, ** 370** (2012), 32-45.

**Duality for nonlinear simply laced groups**

(with Jeffrey Adams)
arxiv
or
pdf

*Compositio Mathematica,* **148** (2012), no. 03, 931-965.

**Duality for GL(n,R) and the degenerate
affine Hecke algebra for gl(n)**

(with Dan Ciubotaru) arxiv
or pdf

*American Journal of Math.* **134** (2012), no. 1, 141-170.

**Regular orbits of symmetric subgroups on
partial flag varieties**

(with D. Ciubotaru and K. Nishiyama)
arxiv
or
pdf

* Representation
Theory, Complex Analysis, and Integral Geometry Vol. 2*

Progress in Mathematics, Birkhauser (2012), 61-86.

**Stable combinations of special unipotent representations**

(with Dan Barbasch)
arxiv or
pdf

*Contemp. Math.* **557** (2011), 213-228.

**Functors for unitary representations of
real classical groups and affine Hecke algebras**

(with Dan Ciubotaru) arxiv
or
pdf

*Advances in Math* **227** (2011), no. 4, 1585-1611.

**Pattern avoidence and smoothness for orbits
of a symmetric subgroup in the flag variety**

(with W. M. McGovern) arxiv
or
pdf

*Journal of Algebra,* **322** (2009), 2713-2730.

**Integrals over the Springer fiber
for sl(n,C)** pdf

a stand-alone version of an appendix which appeared in

*Representation Theory,* **12** (2008), 403-434.

**Leading term cycles of Harish-Chandra
modules and partial orders on components of the Springer fiber**
pdf

* Compositio Mathematica*, **143** (2007), 515-540.

**Some small unipotent representations
of indefinite orthogonal groups and the theta correspondence**

(with Annegret Paul) pdf

*University of Aarhus
Publication Series, ***48** (2007), 103-125.

**Derived functor modules arising as large
constituents of degenerate principal series**

(with Hisayosi Matumoto) pdf

*Compositio Mathematica, ***143** (2007), 222-256.

**
Shimura correspondences for split real
groups**

(with Jeffrey Adams, Dan Barbasch, Annegret Paul, and David Vogan)
pdf

*Journal of the American Math
Society, ***20** (2007), 701-751.

**
Kazhdan-Lusztig
algorithms for nonlinear Lie groups and
applications to Kazhdan-Patterson lifting**

(with David Renard) pdf

*American Journal of Mathematics, *
**127 **(2005), 911-971.

**Symplectic
and orthogonal Robinson-Schensted algorithms**
pdf

*Journal of Algebra, *286 (2005), 386-404.

**Richardson
orbits for real groups**
pdf

*Journal of Algebra, *286
(2005), 361-385.

**Some
small unipotent representations of indefinite orthogonal groups**
pdf

* Journal of Functional Analysis*, **213** (2004),
290-320.

** Special
unipotent representations and the Howe correspondence**
pdf

University of Aarhus
Publication Series, 47
(2004), 210-230.

**Irreducible
genuine characters of the metaplectic group
II:
Functoriality**

(with David Renard) pdf

*Journal für die reine und angewandte Mathematik*,
volume 557 (2003), 121-158.

** One
dimensional representations of U(p,q) and the Howe
correspondence **

(with Annegret Paul) pdf

*Journal of Functional Analysis*, 195 (2002), no. 1, 129--166.

**Annihilators
and associated varieties of A_q(lambda) modules
for U(p,q) **
pdf

*Compositio Mathematica*, 129
(2001), no. 1, 1-45.

**Irreducible
genuine characters of the metaplectic group:
Kazhdan-Lusztig algorithm and Vogan duality**

(with David Renard) pdf

*Representation Theory,* 4
(2000), 245--295.

**Nash equilibria for an evolutionary language game**
(with Martin Nowak)
pdf

*Journal of Mathematical Biology,*41 (2000), no. 2, 172--188.

**Representations
of semisimple Lie groups**

(with Anthony W. Knapp)
pdf

in *Representation theory of Lie groups (Park City, UT, 1998)*,

IAS/Park City Mathematical Series, 8
(2000), 7-87.

** Generalized
Robinson-Schensted algorithms for real Lie
groups** pdf

*International Math Research
Notices*, 1999, no. 15,
803-834.

** The adjoint representation in rings of functions**

(with Eric Sommers)
pdf

*Representation Theory*, 1 (1997), 182-189.

**Fourier series of radial functions in several variables, **

(with Mark Pinsky and Nancy Stanton)
ps

*Journal of Functional Analysis*, 116 (1993), no. 1, 111-132.

Back to the top.

**Some lecture notes:**

** Parametrizing even real nilpotent orbits
using ATLAS**
pdf

Unpublished notes from a lecture at University of Maryland workshop,
March, 2008. A few small corrections made in 2017.

**Notes
on cells and special unipotent representations**
pdf

Unpublished notes from a lecture at an AIM workshop, July, 2007.

Based partially on notes taken by Patrick Polo. I made some small correctionsin 2017.

**On the computation of characteristic cycles of Harish-Chandra modules**
pdf

Unpublished notes from a lecture an AIM workshop, July, 2006.

**
Computing Real Weyl Groups**
pdf

Unpublished notes from a lecture given by David Vogan at an AIM work
shop, July, 2006.

**Computing K-type multiplicities in standard
modules (after Vogan)**
pdf

Unpublished notes from lectures at an AIM workshop, July,
2005.

**Branching Laws**
pdf

Unpubilshed notes from an AIM workshop, July, 2003.

Notes by David Vogan.

**Unitary representations of U(p,q)**
pdf

Notes from a talk at the AMS-SRC conference
"Representation theory of real and p-adic reductive groups"

University of Washington, July, 1997.

Back to the top.

**Some slides:**

**Cohomological Induction**
pdf

Slides from a talk at a
2017 Atlas of Lie Groups workshop.

Relations between unitary representations of real and
p-adic groups,

Slides from my talk at David Vogan's Birthday
Conference, 2014.

**Kazhdan-Lusztig-Vogan polynomials
and
applications**
pdf

Slides from a Colloquium at the University of Washington, October, 2007.

**Matching Kazhdan-Lustzig
polynomials for
GL(n,F)** pdf

Slides from a lecture at an AIM workshop, July, 2007.

**Starting a High School Math Circle**

Slides from an invited address at an MAA meeting, March, 2006.

In ppt format
ppt

Back to the top.

**Some conferences I helped organize:**

**SL(2,R)
Minicourse (May 2006)**

(with Casselman and Milicic)

Minicourse
Homepage

** Representation Theory of Real Lie Groups (June 2006, Snowbird UT)
**

(with Arthur and Schmid)

Conference Homepage

Conference
Proceedings (coedited with Arthur and Schmid):
published in the AMS series **Contemporary Mathematics**, volume
472, 2008.

** Representations of Reductive Groups (May 2014, MIT)
**

(with Bezrukavnikov, Etingof, Lusztig, and Nevins))

Conference Homepage

Conference Proceedings (coedited with Nevins):
publihsed in the Birkhauser/Springer **Progress in Mathematics** book series (PM, volume 312)

Back to the top.

**Some students:**

**Scott Crofts**, PhD 2009:
Duality for the universal cover of
Spin(2n+1,2n).

**Casey Johnson**, PhD 2010:
Enhanced nilpotent representations of a cyclic quiver.

**Ben Trahan**, PhD 2011:
Functors for real and p-adic metaplectic groups.

**Matt Housley**, PhD 2011:
Polynomial representations and associated cycles of indefinite unitary groups.

**Kei Yuen Chan**, PhD 2014:
Extensions between modules for the graded affine Hecke algbera.

**Adam Brown**, PhD 2019:
Arakawa-Suzuki functors for Whittaker modules.

**Sean McAfee**, PhD 2019:
Twisted cells for real reductive groups.

In progress: **
Chengyu Du,
**

**
Back to the top.
**

**
**

**Some miscellanea:**

**In Math, Confidence Doesn't Count**

An op-ed piece for the *Salt Lake Tribune*
html

**Representation
Theory**

an electronic journal of the AMS

Back to the top.

The above material is based upon work partially supported by NSF
grants DMS-0071606, DMS-0300106, DMS-0554118, DMS-0968275,
DMS-0968060, and DMS-1302237, NSA Grant
MSFP-06Y-095, and the Simons Foundation.