Representation Theory

New submissions

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New submissions for Wed, 8 May 24

[1]  arXiv:2405.03973 [pdf, ps, other]

Title: Restricting Rational Modules to Frobenius Kernels

Authors: Christopher P. Bendel, Daniel K. Nakano, Cornelius Pillen, Paul Sobaje

Subjects: Representation Theory (math.RT); Group Theory (math.GR)

Let $G$ be a connected reductive group over an algebraically closed field of characteristic $p>0$. Given an indecomposable G-module $M$, one can ask when it remains indecomposable upon restriction to the Frobenius kernel $G_r$, and when its $G_r$-socle is simple (the latter being a strictly stronger condition than the former). In this paper, we investigate these questions for $G$ having an irreducible root system of type A. Using Schur functors and inverse Schur functors as our primary tools, we develop new methods of attacking these problems, and in the process obtain new results about classes of Weyl modules, induced modules, and tilting modules that remain indecomposable over $G_r$.

[2]  arXiv:2405.04410 [pdf, ps, other]

Title: Almost special representations of Weyl groups

Authors: G. Lusztig

Comments: 18 pages

Subjects: Representation Theory (math.RT)

Let $c$ be the family of irreducible representations of a Weyl group $W$ corresponding to a two-sided cell of $W$. We define a subset $A_c$ of $c$ which contains the special representation of $W$ in $c$ and is in canonical bijection with the set of constructible representations of $W$ attached to $c$.

Cross-lists for Wed, 8 May 24

[3]  arXiv:2405.04137 (cross-list from math.QA) [pdf, ps, other]

Title: Deformed quantum vertex algebra modules associated with braidings

Authors: Lucia Bagnoli, Slaven Kožić

Comments: 25 pages, comments are welcome

Subjects: Quantum Algebra (math.QA); Representation Theory (math.RT)

We introduce the notion of deformed quantum vertex algebra module associated with a braiding map. We construct two families of braiding maps over the Etingof-Kazhdan quantum vertex algebras associated with the rational $R$-matrices of classical types. We investigate their properties and demonstrate the applications of the corresponding deformed modules to the (generalized) Yangians and reflection algebras.

Replacements for Wed, 8 May 24

[4]  arXiv:1904.01884 (replaced) [src]

Title: Projection of root systems

Authors: Sarah Dijols

Comments: The computations by hand concerning the exceptional groups were incomplete and contained a few errors leading to incorrect results in some cases

Subjects: Representation Theory (math.RT)

[5]  arXiv:2308.00550 (replaced) [pdf, ps, other]

Title: Quantum difference equation for the affine type $A$ quiver varieties I: General Construction

Authors: Tianqing Zhu

Comments: 62 pages, typo corrected, Proposition 2.13 and Lemma 3.3 has been corrected, Update with an appendix of the rationality of the R-matrix. References added

Subjects: Representation Theory (math.RT); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Algebra (math.QA)

[6]  arXiv:2310.13621 (replaced) [pdf, ps, other]

Title: Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence

Authors: Shigeo Koshitani, Caroline Lassueur, Benjamin Sambale

Comments: Revised version, 25 pages

Subjects: Representation Theory (math.RT); Group Theory (math.GR)

[7]  arXiv:2311.06173 (replaced) [pdf, ps, other]

Title: Two vertex geometrically irreducible algebras

Authors: Grzegorz Bobinski, Grzegorz Zwara

Subjects: Representation Theory (math.RT)

[8]  arXiv:2311.11078 (replaced) [pdf, other]

Title: A Lie group analog for the Monster Lie algebra

Authors: Lisa Carbone, Elizabeth Jurisich, Scott H. Murray

Subjects: Representation Theory (math.RT); Group Theory (math.GR)

[9]  arXiv:2404.18236 (replaced) [pdf, ps, other]

Title: Unbounded $\mathfrak{sl}_3$-laminations around punctures

Authors: Tsukasa Ishibashi, Shunsuke Kano

Comments: 57 pages, 26 figures. v2: added a comment on the Roger--Yang relations in p.42. arXiv admin note: text overlap with arXiv:2204.08947

Subjects: Representation Theory (math.RT); Geometric Topology (math.GT); Quantum Algebra (math.QA)

[10]  arXiv:2405.02956 (replaced) [pdf, ps, other]

Title: Generalized electrical Lie algebras

Authors: Arkady Berenstein, Azat Gainutdinov, Vassily Gorbounov

Comments: AmsLaTeX, 20 pages, misprints corrected

Subjects: Representation Theory (math.RT); Rings and Algebras (math.RA)

[11]  arXiv:2405.03395 (replaced) [pdf, ps, other]

Title: A geometric realization for maximal almost pre-rigid representations over type $\mathbb{D}$ quivers

Authors: Jianmin Chen, Yiting Zheng

Subjects: Representation Theory (math.RT)

[12]  arXiv:2004.01871 (replaced) [pdf, ps, other]

Title: Good Basic Invariants and Frobenius Structures

Authors: Ikuo Satake

Comments: 24 pages, added section 4 examples

Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG); Representation Theory (math.RT)

[13]  arXiv:2004.03587 (replaced) [pdf, ps, other]

Title: Good Basic Invariants for Elliptic Weyl Groups and Frobenius Structures

Authors: Ikuo Satake

Comments: 32 pages. arXiv admin note: text overlap with arXiv:2004.01871. Rewrote section 6;added appendices

Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG); Representation Theory (math.RT)

• New submissions
• Cross-lists
• Replacements