Construction of Irreducible Representations over Khovanov-Lauda-Rouquier Algebras of Finite Classical Type [PDF]
, 2011 We give an explicit construction of irreducible modules over Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^{\lambda}$ for finite classical types using a crystal basis theoretic approach.
G. Benkart +3 more
semanticscholar +1 more source
On irreducible representations of compact $p$-adic analytic groups [PDF]
, 2011 We prove that the canonical dimension of a coadmissible representation of a semisimple $p$-adic Lie group in a $p$-adic Banach space is either zero or at least half the dimension of a non-zero coadjoint orbit.
K. Ardakov, S. Wadsley
semanticscholar +1 more source
European Physical Journal C: Particles and Fields, 2018 We discuss properties of fuzzy de Sitter space defined by means of algebra of the de Sitter group $$\text {SO}(1,4)$$ SO(1,4) in unitary irreducible representations.
Maja Burić +2 more
doaj +1 more source
On the classification of irreducible representations of affine Hecke algebras with unequal parameters [PDF]
, 2010 Introduction 31 Preliminaries 101.1 Root systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2 Affine Hecke algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3 Graded Hecke algebras . . . . . . . . . . . . . . . . . .
M. Solleveld
semanticscholar +1 more source
Automorphy lifting with adequate image
Forum of Mathematics, Sigma, 2023 Let F be a CM number field. We generalise existing automorphy lifting theorems for regular residually irreducible p-adic Galois representations over F by relaxing the big image assumption on the residual representation.
Konstantin Miagkov, Jack A. Thorne
doaj +1 more source
Unitary irreducible representations of SL(2,{C)} in discrete and continuous SU(1,1) bases [PDF]
, 2010 We derive the matrix elements of generators of unitary irreducible representations of SL (2,C) with respect to basis states arising from a decomposition into irreducible representations of SU(1,1).
Florian Conrady, J. Hnybida
semanticscholar +1 more source
On a classification of irreducible admissible modulo $p$ representations of a $p$-adic split reductive group [PDF]
Compositio Mathematica, 2011 We give a classification of irreducible admissible modulo $p$ representations of a split$p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.
N. Abe
semanticscholar +1 more source
A preorder-free construction of the Kazhdan-Lusztig representations of $S_n$, with connections to the Clausen representations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We use the polynomial ring $\mathbb{C}[x_{1,1},\ldots,x_{n,n}]$ to modify the Kazhdan-Lusztig construction of irreducible $S_n$-modules. This modified construction produces exactly the same matrices as the original construction in [$\textit{Invent. Math}$
Charles Buehrle, Mark Skandera
doaj +1 more source
The largest irreducible representations of simple groups [PDF]
, 2010 Answering a question of I. M. Isaacs, we show that the largest degree of irreducible complex representations of any finite non‐abelian simple group can be bounded in terms of the smaller degrees.
M. Larsen, G. Malle, P. Tiep
semanticscholar +1 more source
Representations of the cyclically symmetric q-deformed algebra $so_q(3)$
, 1998 An algebra homomorphism $\psi$ from the nonstandard q-deformed (cyclically symmetric) algebra $U_q(so_3)$ to the extension ${\hat U}_q(sl_2)$ of the Hopf algebra $U_q(sl_2)$ is constructed.
A. U. Klimyk +4 more
core +1 more source