17 citations · 55 across the 12 of their papers we have counts for
12 papers
Macdonald Identities: revisited
K. Iohara, Y. Saito
In this note, after recalling a proof of the Macdonald identities for untwisted affine root systems, we derive the Macdonald identities for twisted affine root systems.
Quantized coordinate rings, PBW-type bases and -boson algebras
Yoshihisa Saito
Recently, Kuniba, Okado and Yamada proved that the transition matrix of PBW-type bases of the positive-half of a quantized universal enveloping algebra coincide…
Toward Berenstein-Zelevinsky data in affine type , part III: Proof of the connectedness
Satoshi Naito, Daisuke Sagaki, Yoshihisa Saito
We prove the connectedness of the crystal, which we introduced in our previous works.
Toward Berenstein-Zelevinsky data in affine type , part II: Explicit description
Satoshi Naito, Daisuke Sagaki, Yoshihisa Saito
In the present paper, we give an explicit description of the affine analogs of Berenstein-Zelevinsky data constructed in our previous paper: Toward Berenstein-Zelevinsky data in af…
Mirković-Vilonen Polytopes and a quiver construction of crystal basis in type
Yoshihisa Saito
In the current paper, we give a quiver theoretical interpretation of Mirković-Vilonen polytopes in type . As a by-product, we give a new proof of the Anderson-Mirković conject…
Toward Berenstein-Zelevinsky data in affine type , I: Construction of affine analogs
Satoshi Naito, Daisuke Sagaki, Yoshihisa Saito
We give (conjectural) analogs of Berenstein-Zelevinsky data for affine type . Moreover, by using these affine analogs of Berenstein-Zelevinsky data, we realize the crystal basis…
Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to
Hiroki Kondo, Yoshihisa Saito
In this paper we study the tensor category structure of the module category of the restricted quantum enveloping algebra associated to . Indecomposable decompositi…
The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials
Saburo Kakei, Michitomo Nishizawa, Yoshihisa Saito +1
We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra . The main ingredient is a special class of the shifted…
Crystal bases and quiver varieties (Geometric construction of crystal bases II)
Yoshihisa Saito
We give a crystal structure on the set of all irreducible components of Lagrangian subvarieties of quiver varieties. One con show that, as a crystal, it is isomorphic to the crysta…
Hirota bilinear forms with 2-toroidal symmetry
K. Iohara, Y. Saito, M. Wakimoto
In this note, we compute Hirota bilinear forms arising from both homogeneous and principal realization of vertex representations of 2-toroidal Lie algebras of type .
Quantum toroidal algebras and their vertex representations
Yoshihisa Saito
We change the definition of the vertex representations. As a result the vertex representations has one parameter.
Geometric Construction of Crystal Bases
Masaki Kashiwara, Yoshihisa Saito
We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the…