Research
Selected publications
Path isomorphisms between quiver Hecke and diagrammatic Bott--Samelson endomorphism algebras, joint with A. Cox and A. Hazi, Advances in Mathematics 2023 (106 pages).
This paper solves Libedinsky-Plaza's conjecture from 2018 and calculates decomposition numbers of cyclotomic Hecke algebras in terms of p-Kazhdan-Lusztig polynomials.
Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions, joint with E. Norton and J. Simental, Journal of the Institute of Mathematics of Jussieu 2022 (52 pages).
This paper extends Berkesh-Griffeth-Sam's conjecture to all cyclotomic Hecke algebras by classifying and constructing all unitary modules of these algebras via BGG resolutions.
On BGG resolutions of unitary simple modules for quiver Hecke and Cherednik algebras, joint with E. Norton and J. Simental, Selecta Mathematica 2022 (71 pages).
This paper solves Berkesh-Griffeth-Sam's conjecture from 2013 by providing BGG resolutions of homogeneous representations of cyclotomic KLR algebras.
The many graded cellular bases of Hecke algebras, American Journal of Mathematics, 2022 (67 pages)
This paper solves Martin-Woodock's conjecture from 2000 and completes Geck-Rouquier's canonical basic set programme for Lusztig orderings on multipartitions.
Multiplicity-free Kronecker products of characters of the symmetric groups, joint with C. Bessenrodt, Advances in Mathematics, 2017 (56 pages).
This paper solves Bessenrodt's conjecture from 1999 by classifying and constructing all multiplicity-free tensor products of characters of symmetric groups.
Preprints
Quiver presentations and isomorphisms of Hecke categories and Khovanov arc algebras, joint with Maud De Visscher, Amit Hazi, and Catharina Stroppel.
The anti-spherical Hecke categories for Hermitian symmetric pairs, joint with Maud De Visscher, Amit Hazi, and Emily Norton.
Oriented Temperley-Lieb algebras and combinatorial Kazhdan-Lusztig theory, joint with Maud De Visscher, Niamh Farrell, Amit Hazi, and Emily Norton.
Canonical bases and new applications of increasing and decreasing subsequences to invariant theory, joint with Steve Doty and Stuart Martin
The partition algebra and plethysm coefficients II: ramified plethysm, joint with Rowena Paget and Mark Wildon.
Published Papers (all available at the arXiv)
The partition algebra and plethysm coefficients I: stability and Foulkes' conjecture, joint with R. Paget, Journal of Algebra.
Splitting Kronecker squares, 2-decomposition numbers, Catalan combinatorics, and the Saxl conjecture, joint with C. Bessenrodt, Algebraic Combinatorics.
The modular Weyl--Kac character formula, joint with E. Norton and A. Hazi, Math Zeitschrift.
The classification of multiplicity-free plethysm products, joint with C.Bessenrodt and R. Paget, Transactions of the AMS.
An integral second fundamental theorem of invariant theory for partition algebras, joint with S. Doty and S. Martin, Representation Theory of the AMS.
Integral Schur--Weyl duality for partition algebras, joint with S. Doty and S. Martin, Algebraic Combinatorics.
Kronecker positivity and 2-modular representation theory, joint with C. Bessenrodt and L. Sutton, Transaction of the AMS.
Path Combinatorics and Light Leaves bases of quiver Hecke algebras, joint with A. Cox, D. Michailidis and A. Hazi, Math Zeitschrift.
The uniqueness of plethystic factorisation, joint with R. Paget, Transactions of the AMS.
An analogue of row removal for diagrammatic Cherednik algebras, joint work with L. Speyer, Math Zeitschrift.
The co-Pieri rule for Kronecker coefficients, joint with M. De Visscher and J. Enyang, Journal of Combinatorial Theory Series A.
Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras, Forum of Mathematics, Sigma.
The cellular second fundamental theorem of invariant theory, joint with J. Enyang and F. M. Goodman, International Mathematical Research Notices.
Simple modules for partition algebras and monotone convergence of Kronecker coefficients, joint with M. De Visscher and J. Enyang, International Mathematical Research Notices.
The integral isomorphism behind first row removal phenomena for Schur algebras, joint with E. Giannelli, Mathematical Proceedings of the Cambridge Philosophical Society.
Kleshchev's decomposition numbers for diagrammatic Cherednik algebras, joint work with L. Speyer, Transactions of the American Mathematical Society.
Diagram algebras, dominance triangularity, and skew cell modules joint with J. Enyang and F. M. Goodman. Journal of the Australian Mathematical Society.
A family of graded decomposition numbers for diagrammatic Cherednik algebras, joint work with A. G. Cox and L. Speyer, International Mathematics Research Notices 2016
The block structure of the partition algebras in characteristic p>0, joint with M. De Visscher and O. King, Algebras and Representation Theory (2015).
Decomposition numbers for Brauer algebras of type G(m,p,n) in characteristic zero, joint with A. G. Cox, Journal of Pure and Applied Algebra, (2014).
The partition algebra and the Kronecker product, joint with M. De Visscher and R. Orellana, Transactions of the American Mathematical Society (2015).
Decomposition numbers of cyclotomic Brauer algebras, joint with A. G. Cox and M. De Visscher, Journal of Algebra 378 (2013).
Decomposition of tensor products of modular irreducible representations for SL_3 for large primes, joint with S.R. Doty and S. Martin, International Electronic Journal of Algebra (2015).
Bases of quasi-hereditary covers of diagram algebras, Mathematical Proceedings of the Cambridge Philosophical Society
Brauer algebras of type C are cellularly stratified algebras, Mathematical Proceedings of the Cambridge Philosophical Society
A reciprocity result for projective indecomposable modules of cellular algebras and BGG algebras, joint with S. Martin, Journal of Lie Theory
Decomposition of tensor products of modular irreducible representations for SL_3 (With an Appendix by C.M. Ringel, joint with S.R. Doty, S. Martin and C.M. Ringel, International Electronic J. Algebra
Other publications
Combinatorial p-Kazhdan–Lusztig theory, joint with A. Hazi, M. De Visscher, and C. Stroppel, Sém. Lothar. Combin. (to appear).
The lattice permutation condition for Kronecker tableaux, joint with M. De Visscher and J. Enyang, Sém. Lothar. Combin. 82B (2020), Art. 5, 12 pp.
The partition algebra and the Kronecker coefficients, joint with M. De Visscher; R. Orellana, DMTCS Proceedings 26th International Conference on FPSAC 2013.
Introduction by the Organizers, Joint with C. Bessenrodt, C. Bowman and A. Kleshchev, Oberwolfach Rep. 39 (2022), DOI: 10.4171/OWR-2022-39.
Introduction by the Organizers, Joint with C. Bessenrodt, C. Bowman, Oberwolfach Rep. 9(2020), DOI: 10.14760/OWR-2020-9.