Eric Marberg

Welcome to my home page! I am an Associate Professor in the department of mathematics at HKUST. My main research interests are in representation theory and algebraic combinatorics.

[Google scholar] [CV]

Email: eric.marberg@gmail.com
Office: Room 3492, Lift 25-26

Current Teaching

Advanced Algebra II (MATH 5112)

Past Courses

Linear Algebra (MATH 2121): Fall 2023, 2022, 2021, 2020, 2019, 2018, 2017
Advanced Algebra II (MATH 5112): Spring 2021
Introduction to Lie Algebras (MATH 5143): Spring 2023, 2022
Coxeter Systems and Iwahori-Hecke Algebras (MATH 6150F): Spring 2017
Combinatorics of Crystal Bases (MATH 6150I): Spring 2020

Research

I've listed my papers and preprints below, organized by year of completion.

2023
57		Crystals for set-valued decomposition tableaux (with Kam Hung Tong) Preprint.
56		Kromatic quasisymmetric functions Preprint.
55		Primed decomposition tableaux and extended queer crystals (with Kam Hung Tong) Preprint.
54		Crystals for shifted key polynomials (with Travis Scrimshaw) Preprint.
53		Key and Lascoux polynomials for symmetric orbit closures (with Travis Scrimshaw) Preprint. An extended abstract for this paper appeared in the proceedings of FPSAC 2023.
2022
52		Insertion algorithms for Gelfand S_n-graphs (with Yifeng Zhang) Preprint.
51		Shifted combinatorial Hopf algebras from K-theory To appear in Algebraic Combinatorics.
50		Combinatorial formulas for shifted dual stable Grothendieck polynomials (with Joel Brewster Lewis) To appear in Forum of Mathematics, Sigma. An extended abstract for this paper appeared in the proceedings of FPSAC 2023.
49		Perfect models for finite Coxeter groups (with Yifeng Zhang) Journal of Pure and Applied Algebra 227 (2023), 107303.
2021
48		Highest weight crystals for Schur Q-functions (with Kam Hung Tong) Combinatorial Theory 3 (2023), no. 2., #6. An extended abstract for this paper appeared in the proceedings of FPSAC 2022.
47		Expanding K-theoretic Schur Q-functions (with Yu-Cheng Chiu) Algebraic Combinatorics, Volume 6 (2023) no. 6, 1419–1445. Conjectures 7.1 and 7.2 are now theorems in paper #50.
46		Extending a word property for twisted Coxeter systems Advances in Applied Mathematics 145 (2023), 102477.
45		Shifted insertion algorithms for primed words Combinatorial Theory 3 (2023), no. 3., #14.
2020
44		Gelfand W-graphs for classical Weyl groups (with Yifeng Zhang) Journal of Algebra 609 (2022), 292–336. An extended abstract for this paper appeared in the proceedings of FPSAC 2021.
43	$Advances in Mathematics$	Gröbner geometry for skew-symmetric matrix Schubert varieties (with Brendan Pawlowski) Advances in Mathematics 405 (2022), 108488. An extended abstract for this paper appeared in the proceedings of FPSAC 2021.
42		Principal specializations of Schubert polynomials in classical types (with Brendan Pawlowski) Algebraic Combinatorics, Volume 4 (2021) no. 2, 273–287. An extended abstract for this paper appeared in the proceedings of FPSAC 2021.
2019
41		Involution pipe dreams (with Zachary Hamaker and Brendan Pawlowski) Canadian Journal of Mathematics, 74 (2022), no. 5, 1310–1346. An extended abstract for this paper appeared in the proceedings of FPSAC 2019.
40		Bumping operators and insertion algorithms for queer supercrystals Selecta Mathematica 28 (2022), Article 36.
39	$Mathematische Zeitschrift$	Enriched set-valued P-partitions and shifted stable Grothendieck polynomials (with Joel Brewster Lewis) Mathematische Zeitschrift 299 (2021), 1929–1972. Conjecture 5.15 is now a theorem in paper #47.
38		On some properties of symplectic Grothendieck polynomials (with Brendan Pawlowski) Journal of Pure and Applied Algebra 225 (2021), 106463.
37	$Advances in Mathematics$	K-theory formulas for orthogonal and symplectic orbit closures (with Brendan Pawlowski) Advances in Mathematics 372 (2020), 107299. Problems 5.5 and 5.6 are now resolved in papers #50 and #53.
36		A symplectic refinement of shifted Hecke insertion Journal of Combinatorial Theory, Series A 173 (2020), 105216. Conjecture 3.23 is now a theorem in this paper of Hiroshima. Conjecture 4.13 is now a theorem in paper #40.
2018
35		Affine transitions for involution Stanley symmetric functions (with Yifeng Zhang) European Journal of Combinatorics 101 (2022), 103463. The Python code referred to in this paper is available online here. An extended abstract for this paper appeared in the proceedings of FPSAC 2019.
34		Linear compactness and combinatorial bialgebras Electronic Journal of Combinatorics 28 (2021), no. 3, Research Paper 9, 47 pages.
33		Bialgebras for Stanley symmetric functions Discrete Mathematics 343 (2020), no. 4, 111778.
32		Stanley symmetric functions for signed involutions (with Brendan Pawlowski) Journal of Combinatorial Theory, Series A 168 (2019), 288–317. An extended abstract for this paper appeared in the proceedings of FPSAC 2019.
31		Atoms for signed permutations (with Zachary Hamaker) European Journal of Combinatorics 94 (2021), 103288.
2017
30		On some actions of the 0-Hecke monoids of affine symmetric groups Journal of Combinatorial Theory, Series A 161 (2019), 178–219. An extended abstract for this paper appeared in the proceedings of FPSAC 2018.
29		Fixed-point-free involutions and Schur P-positivity (with Zachary Hamaker and Brendan Pawlowski) Journal of Combinatorics 11 (2020), no. 1, 65–110.
28		Braid relations for involution words in affine Coxeter groups The Python code referred to in this paper is available online here. Not intended for publication; superseded by this paper of Hansson and Hultman.
27		Schur P-positivity and involution Stanley symmetric functions (with Zachary Hamaker and Brendan Pawlowski) International Mathematics Research Notices, Volume 2019, Issue 17, 5389–5440. Conjecture 5.24 is now a theorem in paper #40.
2016
26		Transition formulas for involution Schubert polynomials (with Zachary Hamaker and Brendan Pawlowski) Selecta Mathematica 24 (2018), 2991–3025. An extended abstract related to this paper appeared in the proceedings of FPSAC 2017.
25		Involution words II: braid relations and atomic structures (with Zachary Hamaker and Brendan Pawlowski) Journal of Algebraic Combinatorics 45 (2017), 701–743.
2015
24		Involution words: counting problems and connections to Schubert calculus for symmetric orbit closures (with Zachary Hamaker and Brendan Pawlowski) Journal of Combinatorial Theory, Series A 160 (2018), 217–260. Conjecture 1.6 is now a theorem in paper #32.
2014
23		Variations of the Poincaré series for affine Weyl groups and q-analogues of Chebyshev polynomials (with Graham White) Advances in Applied Mathematics 82 (2017), 129–154.
22		Bar operators for quasiparabolic conjugacy classes in a Coxeter group Journal of Algebra 453 (2016), 325–363.
21	$Progress in Mathematics$	Comparing and characterizing some constructions of canonical bases from Coxeter systems Representations of Reductive Groups, Progress in Mathematics 312 (2015), 399–436.
2013
20		Strong forms of linearization for Hopf monoids in species Journal of Algebraic Combinatorics 42 (2015), 391–428.
19		Strong forms of self-duality for Hopf monoids in species Transactions of the American Mathematical Society 368 (2016), 5433–5473.
18		Positivity conjectures for Kazhdan-Lusztig theory on twisted involutions: the finite case Journal of Algebra 413 (2014), 198–225. The extended version of Fokko du Cloux's C++ program Coxeter referred to in this paper is available as this archive.
17		Coxeter systems, multiplicity free representations, and twisted Kazhdan-Lusztig Theory PhD Thesis, Massachusetts Institute of Technology (2013). This combines papers #5, #6, #13, #15, #16, and #18 with a little more exposition.
2012
16		Positivity conjectures for Kazhdan-Lusztig theory on twisted involutions: the universal case Representation Theory 18 (2014), 88–116.
15	$Israel Journal of Mathematics$	Isomorphisms, automorphisms, and generalized involution models of projective reflection groups (with Fabrizio Caselli) Israel Journal of Mathematics 199 (2014), 433–483. An extended abstract for this paper in the proceedings of CoMeTa 2013.
14		Crossings and nestings in colored set partitions Electronic Journal of Combinatorics 20 (2013), no. 4, Research Paper 6, 30 pages.
13	$Advances in Mathematics$	How to compute the Frobenius-Schur indicator of a unipotent character of a finite Coxeter system Advances in Mathematics 240 (2013), 484–519. The last open case of Conjecture 1.6, which restates Kottwitz's conjecture, is proved in this paper of Geck and Halls.
2011
12		Actions and identities on set partitions Electronic Journal of Combinatorics 19 (2012), no. 1, Research Paper 28, 31 pages.
11		Heisenberg characters, unitriangular groups, and Fibonacci numbers Journal of Combinatorial Theory, Series A 119 (2012), 882–903.
2010
10		Combinatorial methods of character enumeration for the unitriangular group The Magma code referred to in this paper is located in two files: [one] [two]. Journal of Algebra 345 (2011), 295–323.
9		Exotic characters of unitriangular matrix groups Journal of Pure and Applied Algebra 216 (2012), 239–254.
8	$Advances in Mathematics$	Iterative character constructions for algebra groups Advances in Mathematics 228 (2011), 2743–2765.
7	$Advances in Mathematics$	Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (with Marcelo Aguiar, Carlos André, Carolina Benedetti, Nantel Bergeron, Zhi Chen, Persi Diaconis, Anders Hendrickson, Samuel Hsiao, I. Martin Isaacs, Andrea Jedwab, Kenneth Johnson, Gizem Karaali, Aaron Lauve, Tung Le, Stephen Lewis, Huilan Li, Kay Magaard, Jean-Christophe Novelli, Amy Pang, Franco Saliola, Lenny Tevlin, Jean-Yves Thibon, Nathaniel Thiem, Vidya Venkateswaran, C. Ryan Vinroot, Ning Yan, and Mike Zabrocki) Advances in Mathematics 229 (2012), 2310–2337. An extended abstract for this paper appeared in the proceedings of FPSAC 2011.
6		Automorphisms and generalized involution models of finite complex reflection groups Journal of Algebra 334 (2011), 295–320.
5	$Israel Journal of Mathematics$	Generalized involution models for wreath products Israel Journal of Mathematics 192 (2012), 157–195.
2009
4		Superclasses and supercharacters of normal pattern subgroups of the unipotent upper triangular matrix group Journal of Algebraic Combinatorics 35 (2012), 61–92.
3		A supercharacter analogue for normality Journal of Algebra 332 (2011), 334–365.
2008
2		Constructing Modules of Algebra Groups Undergraduate Honors Thesis, Stanford University (2008). Most of these results reappear, in a significantly improved form, in papers #8, #9, and #10. The upper bound in Theorem 5.1 has been upgraded in this paper of Soffer.
2007
1		Superinduction for pattern groups (with Nathaniel Thiem) Journal of Algebra 321 (2009), 3681–3703.