On Gelfand pairs and degenerate Gelfand-Graev modules of general linear groups of degree two over principal ideal local rings of finite length

Authors: Archita Gupta, Pooja Singla

Source: Journal of Algebra. 684:78-108

Subject Terms: Primary 20G05, Secondary 20C15, 20G25, 15B33, Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2410.21761

The metaplectic representation is faithful

Authors: Chang, Christopher, Hellsten, Simeon, Losada, Mario Marcos, Novac, Sergiu

Source: Journal of Algebra. 684:563-588

Subject Terms: 16D25, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Rings and Algebras, Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2401.04581

Class numbers, congruent numbers and umbral moonshine

Authors: Miranda C.N. Cheng, John F.R. Duncan, Michael H. Mertens

Source: Journal of number theory 277, 201-235 (2025). doi:10.1016/j.jnt.2025.02.007

Subject Terms: High Energy Physics - Theory, Mathematics - Number Theory, High Energy Physics - Theory (hep-th), FOS: Mathematics, FOS: Physical sciences, Number Theory (math.NT), 11F22, 11F37, 11G05, 11G40, 20C34, Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2306.16414
https://publications.rwth-aachen.de/record/1012908

Representation theory of graded algebras given by locally finite quivers

Authors: Zetao Lin, Shiping Liu

Source: Journal of Algebra. 683:672-718

Subject Terms: 16E35, 16G20, 16G70, 16W50, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2409.20392

On the classification of unitary highest weight modules in the exceptional cases

Authors: Pandžić, Pavle, Prlić, Ana, Savin, Gordan, Souček, Vladimír, Tuček, Vít

Source: Journal of Algebra. 684:524-562

Subject Terms: FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2412.06317

Character triples and weights

Authors: Feng, Zhicheng

Source: Journal of Algebra. 684:690-725

Subject Terms: FOS: Mathematics, Group Theory (math.GR), Representation Theory (math.RT), Mathematics - Group Theory, Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2502.00774

Full conformal oscillator representations of odd orthogonal Lie algebras and combinatorial identities

Authors: Zhenyu Zhou, Xiaoping Xu

Source: Journal of Algebra. 681:62-106

Subject Terms: 0103 physical sciences, FOS: Mathematics, 17B10 (Primary) 05A19 (Secondary), 0101 mathematics, Representation Theory (math.RT), 01 natural sciences, Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2212.09966

Nilpotent orbits and their secant varieties

Authors: Panyushev, Dmitri I.

Source: Journal of Algebra. 682:689-722

Subject Terms: Mathematics - Algebraic Geometry, FOS: Mathematics, Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2412.20809

Tensor product Markov chains and Weil representations

Authors: Fulman, Jason, Larsen, Michael, Tiep, Pham Huu

Source: Journal of Algebra. 682:278-314

Subject Terms: Probability (math.PR), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory, Mathematics - Probability

Access URL: http://arxiv.org/abs/2407.12713

Recollements and Gorenstein projective modules for gentle algebras

Authors: Liu, Yu-Zhe, Liu, Dajun, Ma, Xin

Source: Journal of Algebra. 682:545-568

Subject Terms: FOS: Mathematics, 16G10, 16G20, 18G05, Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2409.08686

On the (super)cocenter of cyclotomic Sergeev algebras

Authors: Shuo Li, Lei Shi

Source: Journal of Algebra. 682:824-858

Subject Terms: FOS: Mathematics, Group Theory (math.GR), Representation Theory (math.RT), Mathematics - Group Theory, Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2501.18260

Essential semigroups and branching rules

Authors: Gornitskii, Andrei

Source: Journal of Algebra. 681:190-205

Subject Terms: FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2407.07756

Restricted representations of the twisted N = 2 superconformal algebra

Authors: Haibo Chen, Yucai Su, Yukun Xiao

Source: Journal of Algebra. 681:318-342

Subject Terms: FOS: Mathematics, 0101 mathematics, Representation Theory (math.RT), 01 natural sciences, Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2303.06898

The charge statistic in type A via the affine Grassmannian

Authors: Patimo, Leonardo

Source: Journal of Algebra. 679:169-211

Subject Terms: Affine Grassmannian, Charge statistic, Kostka-Foulkes polynomials, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2412.10562
https://hdl.handle.net/11568/1314027
https://doi.org/10.1016/j.jalgebra.2025.04.036

A reformulation of the conjecture of Prasad and Takloo-Bighash

Authors: Miyu Suzuki

Source: Journal of Algebra. 680:174-204

Subject Terms: Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2312.16393

A converse theorem for quasi-split even special orthogonal groups over finite fields

Authors: Alexander Hazeltine

Source: Journal of Number Theory. 279:479-511

Subject Terms: Mathematics - Number Theory, 20C33, 20G40, FOS: Mathematics, Number Theory (math.NT), Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2501.16338

From classes in the Weyl group to strata

Authors: Lusztig, G.

Source: Journal of Algebra. 687:655-672

Subject Terms: FOS: Mathematics, Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2408.09584

Hook theorem for superalgebras with superinvolution or graded involution

Authors: Sviridova, Irina, Silva, Renata A.

Source: Journal of Algebra. 687:117-150

Subject Terms: Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Rings and Algebras, Representation Theory (math.RT), 16R10, 16R50, 16W50, 16W55, 16W10, Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2501.01562

Ribbon blocks for centraliser algebras of symmetric groups

Authors: Matthew Fayers, Lorenzo Putignano

Source: Journal of Algebra. 685:271-312

Subject Terms: FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2502.13867

The homological spectrum and nilpotence theorems for Lie superalgebra representations

Authors: Hamil, Matthew H., Nakano, Daniel K.

Source: Journal of Algebra. 685:801-830

Subject Terms: FOS: Mathematics, Mathematics - Category Theory, Category Theory (math.CT), 18M05, Group Theory (math.GR), Representation Theory (math.RT), Mathematics - Group Theory, Mathematics - Representation Theory

Access URL: http://arxiv.org/abs/2404.04457