382 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Kyoto UniversityJP369 papers
- The University of TokyoJP33 papers
- Korea Institute for Advanced StudyKR13 papers
- The University of OsakaJP12 papers
- Centre National de la Recherche ScientifiqueFR10 papers
- Nagoya UniversityJP10 papers
- Seoul National UniversityKR10 papers
- Yukawa Institute for Theoretical PhysicsJP10 papers
- Fujian Normal UniversityCN8 papers
- Kavli Institute for the Physics and Mathematics of the UniverseJP8 papers
- National Research University Higher School of EconomicsRU8 papers
- Hiroshima UniversityJP7 papers
30 papers · 1 filter
Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra
Sven Möller, Nils R. Scheithauer
We prove a dimension formula for the weight-1 subspace of a vertex operator algebra obtained by orbifolding a strongly rational, holomorphic vertex oper…
Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in
Sven Möller
Borcherds-Kac-Moody algebras generalise finite-dimensional, simple Lie algebras. Scheithauer showed that there are exactly ten Borcherds-Kac-Moody algebras whose denominator identi…
Quantum Langlands duality of representations of W-algebras
Tomoyuki Arakawa, Edward Frenkel
We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands Program and some related results.
W-algebras as coset vertex algebras
Tomoyuki Arakawa, Thomas Creutzig, Andrew R. Linshaw
We prove the long-standing conjecture on the coset construction of the minimal series principal -algebras of types in full generality. We do this by first establishing Fei…
Coproduct for the Yangian of an affine Kac-Moody algebra
Nicolas Guay, Hiraku Nakajima, Curtis Wendlandt
Given an affine Kac-Moody algebra, we explain how to construct a coproduct for its associated Yangian. In order to prove that this coproduct is an algebra homomorphism, we obtain,…
Singular vectors of super Virasoro algebra via Uglov symmetric functions
Shintarou Yanagida
We give a proof of the conjecture by Belavin, Bershtein and Tarnopolsky, which claims that a bosonization of singular vectors of super Virasoro algebra can be identified with…
Riordan trees and the homotopy weight system
Jean-Baptiste Meilhan, Sakie Suzuki
The purpose of this paper is twofold. On one hand, we introduce a modification of the dual canonical basis for invariant tensors of the 3-dimensional irreducible representation of…
Cyclicity for categorified quantum groups
Anna Beliakova, Kazuo Habiro, Aaron D. Lauda +1
We equip the categorified quantum group attached to a KLR algebra and an arbitrary choice of scalars with duality functor which is cyclic, that is, such that f=f^** for all 2-morph…
Current algebras and categorified quantum groups
Anna Beliakova, Kazuo Habiro, Aaron D. Lauda +1
We identify the trace, or 0th Hochschild homology, of type ADE categorified quantum groups with the corresponding current algebra of the same type. To prove this, we show that 2-re…
Trace decategorification of categorified quantum sl(2)
Anna Beliakova, Kazuo Habiro, Aaron D. Lauda +1
The trace or the th Hochschild--Mitchell homology of a linear category may be regarded as a kind of decategorification of . We compute traces of the t…
Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions
Shintarou Yanagida
We give a proof of Awata and Yamada's conjecture for the explicit formula of Whittaker vector of the deformed Virasoro algebra realized in the Fock space. The formula is expressed…
Bethe subalgebras in Hecke algebra and Gaudin models
A. P. Isaev, Anatol N. Kirillov
The generating function for elements of the Bethe subalgebra of Hecke algebra is constructed as Sklyanin's transfer-matrix operator for Hecke chain. We show that in a special class…
Rationality of W-algebras: principal nilpotent cases
Tomoyuki Arakawa
We prove the rationality of all the minimal series principal W-algebras discovered by Frenkel, Kac and Wakimoto in 1992, thereby giving a new family of rational and C_2-cofinite ve…
Rationality of admissible affine vertex algebras in the category O
Tomoyuki Arakawa
We study the vertex algebras associated with modular invariant representations of affine Kac-Moody algebras at fractional levels, whose simple highest weight modules are classified…
Two-sided BGG resolutions of admissible representations
Tomoyuki Arakawa
We prove the conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions of G-integrable admissible representations of affine Kac-Moody algebras at fracti…
Quiver varieties and tensor products, II
Hiraku Nakajima
We define a family of homomorphisms on a collection of convolution algebras associated with quiver varieties, which gives a kind of coproduct on the Yangian associated with a symme…
Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras
Seok-Jin Kang, Masaki Kashiwara
In this paper, we prove Khovanov-Lauda's cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let be the quantum group associated with a symmet…
Rationality of Bershadsky-Polyakov vertex algebras
Tomoyuki Arakawa
We prove the conjecture of Kac-Wakimoto on the rationality of exceptional W-algebras for the first non-trivial series, namely, for the Bershadsky-Polyakov vertex algebras $W_3^{(2)…
Associated varieties of modules over Kac-Moody algebras and -cofiniteness of W-algebras
Tomoyuki Arakawa
First, we establish the relation between the associated varieties of modules over Kac-Moody algebras \hat{g} and those over affine W-algebras. Second, we prove the Feigin-Frenkel c…
Quiver varieties and cluster algebras
Hiraku Nakajima
Motivated by a recent conjecture by Hernandez and Leclerc [arXiv:0903.1452], we embed a Fomin-Zelevinsky cluster algebra [arXiv:math/0104151] into the Grothendieck ring R of the ca…
Representation theory of W-algebras, II: Ramond twisted representations
Tomoyuki Arakawa
We study the Ramond twisted representations of the affine W-algebra W^k(g,f) in the case that f admits a good even grading. We establish the vanishing and the almost irreducibility…
Affine Geometric Crystals and Limit of Perfect Crystals
Masaki Kashiwara, Toshiki Nakashima, Masato Okado
For every non-exceptional affine Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra-discret…
A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups
Anatol. N. Kirillov, Toshiaki Maeno
We give a description of the (small) quantum cohomology ring of the flag variety as a certain commutative subalgebra in the tensor product of the Nichols algebras. Our main result…
On the eigenstates of the elliptic Calogero-Moser model
Kouichi Takemura
It is known that the trigonometric Calogero-Sutherland model is obtained by the trigonometric limit (τ\to \sqrt{-1} \infty) of the elliptic Calogero-Moser model, where (1,τ) is a b…