Research Institute for Mathematical Sciences, Kyoto University

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most citedTopological Lattice Models in Four Dimensions

382 citations

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math.RT2020

Kazhdan-Lusztig conjecture via Zastava spaces

Alexander Braverman, Michael Finkelberg, Hiraku Nakajima

We deduce the Kazhdan-Lusztig conjecture on the multiplicities of simple modules over a simple complex Lie algebra in Verma modules in category O from the equivariant geometric Sat…

math.RT2020★ 22 cited

Affine Super Yangians and Rectangular $W$ -superalgebras

Mamoru Ueda

In this paper, we construct a homomorphism from the affine super Yangian $Y_{\ve_1,\ve_2}(\widehat{\mathfrak{sl}}(m|n))$ to the universal enveloping algebra of the rectangular $W$ -…

math.RT2019★ 10 cited

Graded quiver varieties and singularities of normalized R-matrices for fundamental modules

Ryo Fujita

We present a simple unified formula expressing the denominators of the normalized R-matrices between the fundamental modules over the quantum loop algebras of type ADE. It has an i…

math.RT2019★ 37 cited

Monoidal categorification and quantum affine algebras

Masaki Kashiwara, Myungho Kim, Se-jin Oh +1

We introduce and investigate new invariants on the pair of modules $M$ and $N$ over quantum affine algebras $U_{q}^{'} (g)$ by analyzing their associated R-matrices. From new…

math.RT2019★ 5 cited

Stability and Indecomposability of the Representations of Quivers of $A_{n}$ -type

Pengfei Huang, Zhi Hu

In his paper \cite{MR1}, Markus Reineke proposed a conjecture that there exists a stable weight system $Θ$ for every indecomposable representation of Dynkin type quiver. In this pa…

math.RT2019★ 12 cited

Cluster realizations of Weyl groups and higher Teichmüller theory

Rei Inoue, Tsukasa Ishibashi, Hironori Oya

For a symmetrizable Kac-Moody Lie algebra $g$ , we construct a family of weighted quivers $Q_{m} (g)$ ( $m \geq 2$ ) whose cluster modular group $Γ_{Q_m(\mathfrak{g…

math.RT2018★ 2 cited

Global crystal bases for integrable modules over a quantum symmetric pair of type AIII

Hideya Watanabe

In this paper, we study basic properties of global $$ -crystal bases for integrable modules over a quantum symmetric pair coideal subalgebra $U^{}$ associated t…

math.RT2018★ 13 cited

Line bundles over Coulomb branches

Alexander Braverman, Michael Finkelberg, Hiraku Nakajima

This is the third companion paper of arXiv:1601.03586. When a gauge theory has a flavor symmetry group, we construct a partial resolution of the Coulomb branch as a variant of the…

math.RT2018★ 13 cited

Singular support of a vertex algebra and the arc space of its associated scheme

Tomoyuki Arakawa, Andrew R. Linshaw

Attached to a vertex algebra $V$ are two geometric objects. The associated scheme of $V$ is the spectrum of Zhu's Poisson algebra $R_{V}$ . The singula…

math.RT2018★ 9 cited

Arc spaces and chiral symplectic cores

Tomoyuki Arakawa, Anne Moreau

We introduce the notion of chiral symplectic cores in a vertex Poisson variety, which can be viewed as analogs of symplectic leaves in Poisson varieties. As an application we show…

math.RT2018★ 1 cited

Quantum Schur duality of affine type C with three parameters

Zhaobing Fan, Chun-Ju Lai, Yiqiang Li +3

We establish a three-parameter Schur duality between the affine Hecke algebra of type C and a coideal subalgebra of quantum affine $sl_{n}$ . At the equal parameter special…

math.RT2017★ 6 cited

Representation theory of W-algebras and Higgs branch conjecture

Tomoyuki Arakawa

We survey a number of results regarding the representation theory of $W$ -algebras and their connection with the resent development of the four dimensional $N = 2$ superconformal fiel…

math.RT2017★ 5 cited

Associated varieties and Higgs branches (a survey)

Tomoyuki Arakawa

Associated varieties of vertex algebras are analogue of the associated varieties of primitive ideals of the universal enveloping algebras of semisimple Lie algebras. They not only…

math.RT2017★ 13 cited

Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types

Ryo Fujita

For a Dynkin quiver $Q$ (of type ADE), we consider a central completion of the convolution algebra of the equivariant K-group of a certain Steinberg type graded quiver variety. We…

math.RT2017★ 3 cited

Monoidal categories associated with strata of flag manifolds

Masaki Kashiwara, Myungho Kim, Se-jin Oh +1

We construct a monoidal category $C_{w, v}$ which categorifies the doubly-invariant algebra $^{N^{'} (w)} C [N]^{N (v)}$ associated with Weyl group elements $w$ and $v$ .…

math.RT2016★ 8 cited

Modularity of Relatively Rational Vertex Algebras and Fusion Rules of Principal Affine W-Algebras

Tomoyuki Arakawa, Jethro van Ekeren

We study modularity of the characters of a vertex (super)algebra equipped with a family of conformal structures. Along the way we introduce the notions of rationality and cofiniten…

math.RT2016★ 1 cited

Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras

Tomoyuki Arakawa, Alexander Premet

We use affine W-algebras to quantize Mishchenko-Fomenko subalgebras for centralizers of nilpotent elements in simple Lie algebras under certain assumptions that are satisfied for a…

math.RT2016★ 36 cited

Orbifolds and cosets of minimal $W$ -algebras

Tomoyuki Arakawa, Thomas Creutzig, Kazuya Kawasetsu +1

Let $g$ be a simple, finite-dimensional Lie (super)algebra equipped with an embedding of $s l_{2}$ inducing the minimal gradation on $g$ .…

math.RT2016★ 35 cited

Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras

Ryosuke Kodera, Hiraku Nakajima

We study quantized Coulomb branches of quiver gauge theories of Jordan type. We prove that the quantized Coulomb branch is isomorphic to the spherical graded Cherednik algebra in t…

math.RT2016★ 35 cited

Screening operators for W-algebras

Naoki Genra

Let $g$ be a simple finite-dimensional Lie superalgebra with a non-degenerate supersymmetric even invariant bilinear form, $f$ a nilpotent element in the even part of $\…

math.RT2016★ 23 cited

Weight representations of admissible affine vertex algebras

Tomoyuki Arakawa, Vyacheslav Futorny, Luis Enrique Ramirez

For an admissible affine vertex algebra $V_{k} (g)$ of type $A$ , we describe a new family of relaxed highest weight representations of $V_{k} (g)$ . They are simple…

math.RT2016★ 194 cited

Towards a mathematical definition of Coulomb branches of $3$ -dimensional $N = 4$ gauge theories, II

Alexander Braverman, Michael Finkelberg, Hiraku Nakajima

Consider the $3$ -dimensional $N = 4$ supersymmetric gauge theory associated with a compact Lie group $G_{c}$ and its quaternionic representation $M$ . Physicists study…

math.RT2015★ 21 cited

Cosets of Bershadsky-Polyakov algebras and rational $W$ -algebras of type $A$

Tomoyuki Arakawa, Thomas Creutzig, Andrew R. Linshaw

The Bershadsky-Polyakov algebra is the $W$ -algebra associated to $s l_{3}$ with its minimal nilpotent element $f_{θ}$ . For notational convenience we defi…

math.RT2015★ 3 cited

Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations

A. P. Isaev, A. N. Kirillov, V. O. Tarasov

Commutative sets of Jucys-Murphyelements for affine braid groups of $A^{(1)}, B^{(1)}, C^{(1)}, D^{(1)}$ types were defined. Construction of $R$ -matrix representations of the affine b…

Kazhdan-Lusztig conjecture via Zastava spaces

Affine Super Yangians and Rectangular W-superalgebras

Graded quiver varieties and singularities of normalized R-matrices for fundamental modules

Monoidal categorification and quantum affine algebras

Stability and Indecomposability of the Representations of Quivers of An​-type

Cluster realizations of Weyl groups and higher Teichmüller theory

Global crystal bases for integrable modules over a quantum symmetric pair of type AIII

Line bundles over Coulomb branches

Singular support of a vertex algebra and the arc space of its associated scheme

Arc spaces and chiral symplectic cores

Quantum Schur duality of affine type C with three parameters

Representation theory of W-algebras and Higgs branch conjecture

Associated varieties and Higgs branches (a survey)

Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types

Monoidal categories associated with strata of flag manifolds

Modularity of Relatively Rational Vertex Algebras and Fusion Rules of Principal Affine W-Algebras

Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras

Orbifolds and cosets of minimal W-algebras

Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras

Screening operators for W-algebras

Weight representations of admissible affine vertex algebras

Towards a mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories, II

Cosets of Bershadsky-Polyakov algebras and rational W-algebras of type A

Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations

Affine Super Yangians and Rectangular $W$ -superalgebras

Stability and Indecomposability of the Representations of Quivers of $A_{n}$ -type

Orbifolds and cosets of minimal $W$ -algebras

Towards a mathematical definition of Coulomb branches of $3$ -dimensional $N = 4$ gauge theories, II

Cosets of Bershadsky-Polyakov algebras and rational $W$ -algebras of type $A$