Results 11 to 20 of about 3,794 (38)

A survey on maximal green sequences

, 2020
Maximal green sequences appear in the study of Fomin-Zelevinsky's cluster algebras. They are useful for computing refined Donaldson-Thomas invariants, constructing twist automorphisms and proving the existence of theta bases and generic bases.
Demonet, Laurent, Keller, Bernhard
core   +1 more source

The PBW Filtration, Demazure Modules and Toroidal Current Algebras [PDF]

, 2008
Let $L$ be the basic (level one vacuum) representation of the affine Kac-Moody Lie algebra $\hat{\mathfrak g}$. The $m$-th space $F_m$ of the PBW filtration on $L$ is a linear span of vectors of the form $x_1...
Feigin, Evgeny
core   +5 more sources

From triangulated categories to cluster algebras [PDF]

, 2005
The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of the cluster ...
Caldero, Philippe, Keller, Bernhard
core   +8 more sources

Infinite-dimensional diffusions as limits of random walks on partitions [PDF]

, 2008
The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group. This problem leads to a family {P_z} of probability measures, the z-measures, which depend on the complex parameter z.
A. Borodin, A. Borodin, A. Borodin, A. Borodin, A. Edrei, A. Lascoux, A.D. Wentzell, A.M. Vershik, Alexei Borodin, B. Schmuland, E. Thoma, Grigori Olshanski, I.B. Frenkel, I.G. Macdonald, J. Fulman, J. Lamperti, J.G. Kemeny, L. Overbeck, S. Kerov, S. Kerov, S. Kerov, S.N. Ethier, S.N. Ethier   +22 more
core   +2 more sources

Representations of rational Cherednik algebras

, 2005
This paper surveys the representation theory of rational Cherednik algebras. We also discuss the representations of the spherical subalgebras. We describe in particular the results on category O.
Rouquier, Raphael
core   +1 more source

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

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

Cluster algebras via cluster categories with infinite-dimensional morphism spaces

, 2010
We apply our previous work on cluster characters for Hom-infinite cluster categories to the theory of cluster algebras. We give a new proof of Conjectures 5.4, 6.13, 7.2, 7.10 and 7.12 of Fomin and Zelevinsky's Cluster algebras IV for skew-symmetric ...
Bourbaki, Dehy, Gekhtman, Keller, Pierre-Guy Plamondon, Sherman, Zelevinsky   +6 more
core   +2 more sources

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