Results 21 to 30 of about 176 (51)
, 2010 Let g be a simple complex Lie algebra and let e be a nilpotent element of g. It was conjectured by Premet in [P07i] that the finite W-algebra U(g; e) admits a 1-dimensional representation, and further work [L10, P08] has reduced this conjecture to the ...
Ubly, Glenn
core +1 more source
COMPLEX SEMISIMPLE QUANTUM GROUPS AND REPRESENTATION THEORY [PDF]
, 2019 This book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups.
Yuncken, Robert, Voigt, Christian
core +1 more source
Automorphisms and twisted vertex operators [PDF]
, 1987 This work is an examination of various aspects of twisted vertex operator representations of Kac-Moody algebras. It starts with an introduction to Kac-Moody algebras and string theories, including a discussion of the propagation of strings on orbifolds ...
Myhill, R.G, Myhill, Richard Graham
core
Invariant algebras and completely reducible representations [PDF]
, 1994 We give a general construction of affine noetherian algebras with the property that every finite dimensional representation is completely reducible. Starting from enveloping algebras of semi simple Lie algebras in characteristic zero we obtain explicit ...
Kraft, Hanspeter, Small, Lance W.
core
Algebra 4: Lie algebras, Chevalley groups, and their representations
, 2021 This book, the fourth book in the four-volume series in algebra, discusses Lie algebra and representation theory in detail. It covers topics such as semisimple Lie algebras, root systems, representation theory of Lie algebra, Chevalley groups and ...
Lal, Ramji
core +1 more source
The local Langlands correspondence for inner forms of SL_n [PDF]
, 2016 Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group SLn(F). It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for SLn(F) enhanced with ...
Aubert, Anne-Marie +11 more
core +3 more sources
Beurling–Fourier algebras of q-deformations of compact semisimple Lie groups and complexification [PDF]
We study Beurling–Fourier algebras of q-deformations of compact semisimple Lie groups. In particular, we show that the space of irreducible representations of the function algebras of their Drinfeld doubles is exhausted by the irreducible representations
Voigt, Christian, Lee, Heon
core +4 more sources
Quantized semisimple Lie groups [PDF]
summary:The goal of this expository paper is to give a quick introduction to $q$-deformations of semisimple Lie groups. We discuss principally the rank one examples of $\mathcal{U}_q(\mathfrak{sl}_2)$, $\mathcal{O}(\mathrm{SU}_q(2))$, $\mathcal{D ...
Yuncken, Robert, Fioresi, Rita
core +1 more source
On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
wiley +1 more source
Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p$p$
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let G$G$ be a finite group and p$p$ be a prime. We establish an upper bound for the derived length of a Sylow p$p$‐subgroup of G$G$ in terms of the number of irreducible characters of G$G$ whose degrees are divisible by p$p$. We also prove that if B$B$ is a p$p$‐block of a finite p$p$‐solvable group G$G$ with defect group D$D$, then the ...
James P. Cossey +3 more
wiley +1 more source