Results 11 to 20 of about 3,969 (32)

Principal series for general linear groups over finite commutative rings

, 2017
We construct, for any finite commutative ring $R$, a family of representations of the general linear group $\mathrm{GL}_n(R)$ whose intertwining properties mirror those of the principal series for $\mathrm{GL}_n$ over a finite field.Comment: 10 ...
Brown, André EX, Ch'ng, Quee-Lim, Currie, Michael, Grundy, Laura J, Hokanson, Jim, Javer, Avelino, Kerr, Rex, Lee, Chee Wai, Li, Chris, Li, Kezhi, Schafer, William R, Yemini, Eviatar   +11 more
core   +8 more sources

Tropicalization method in cluster algebras

, 2012
This is a brief survey on the recently developing tropicalization method in cluster algebras and its applications to the periodicities of Y-systems and the associated dilogarithm identities.Comment: 21 pages, prepared for the proceedings of "Tropical ...
Nakanishi, Tomoki
core   +1 more source

Generic cluster characters

, 2011
Let $\CC$ be a Hom-finite triangulated 2-Calabi-Yau category with a cluster-tilting object $T$. Under a constructibility condition we prove the existence of a set $\mathcal G^T(\CC)$ of generic values of the cluster character associated to $T$.
Amiot, Assem, Assem, Brüstle, Buan, Buan, Buan, Buan, Caldero, Caldero, Caldero, Caldero, Caldero, Cerulli, Dehy, Derksen, Derksen, Ding, Dupont, Dupont, Fomin, Fomin, Fu, Geiss, Geiss, Grégoire Dupont, Igusa, Kac, Kac, Keller, Keller, Keller, Lampe, Nakajima, Palu, Palu, Plamondon, Schofield, Sherman   +38 more
core   +1 more source

Random Strict Partitions and Determinantal Point Processes

, 2010
In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty).
Petrov, Leonid
core   +1 more source

BPS Algebras, Genus Zero, and the Heterotic Monster

, 2017
In this note, we expand on some technical issues raised in \cite{PPV} by the authors, as well as providing a friendly introduction to and summary of our previous work.
Paquette, Natalie M., Persson, Daniel, Volpato, Roberto   +2 more
core   +1 more source

Sylvester-t' Hooft generators of sl(n) and sl(n|n), and relations between them

, 2006
Among the simple finite dimensional Lie algebras, only sl(n) possesses two automorphisms of finite order which have no common nonzero eigenvector with eigenvalue one.
A. A. Belavin, A. A. Belavin, A. I. Kostrikin, A. I. Kostrikin, C. Sachse, C. Zachos, C.-Y. Mou, D. A. Leites, D. Fairlie, D. Fairlie, D. Leites, D. Leites, G. Hooft ’t, H. Weyl, J. Hoppe, J. Miller, J. Moyal, J. Sylvester, L. A. Ferreira, P. Grozman, P. Grozman, P. Grozman, V. Zeitlin, Y. Buhturin   +23 more
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Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver

, 2017
Reflection states are introduced in the vertical and horizontal modules of the Ding-Iohara-Miki (DIM) algebra (quantum toroidal $\mathfrak{gl}_1$). Webs of DIM representations are in correspondence with $(p,q)$-web diagrams of type IIB string theory ...
Bourgine, Jean-Emile, Fukuda, Masayuki, Matsuo, Yutaka, Zhu, Rui-Dong   +3 more
core   +1 more source

Deligne categories and the limit of categories $Rep(GL(m|n))$

, 2019
For each integer $t$ a tensor category $V_t$ is constructed, such that exact tensor functors $V_t \longrightarrow C$ classify dualizable $t$-dimensional objects in $C$ not annihilated by any Schur functor.
Entova-Aizenbud, Inna, Hinich, Vladimir, Serganova, Vera   +2 more
core   +1 more source

A brief review of abelian categorifications

, 2007
This article contains a review of categorifications of semisimple representations of various rings via abelian categories and exact endofunctors on them.
Khovanov, Mikhail, Mazorchuk, Volodymyr, Stroppel, Catharina   +2 more
core   +1 more source

Twisted Chiral Algebras of Class S and Mixed Feigin-Frenkel Gluing. [PDF]

Commun Math Phys, 2023
Beem C, Nair S.
europepmc   +1 more source