98 citations · 277 across the 12 of their papers we have counts for
12 papers
Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal
Yusuke Ohkubo
It is known that the -deformed Virasoro algebra can be constructed from a certain representation of the quantum toroidal algebra. In this paper, we apply the s…
Branching Formula for -Toda Function of Type B
Ayumu Hoshino, Yusuke Ohkubo, Jun'ichi Shiraishi
We present a proof of the explicit formula for the asymptotically free eigenfunctions of the -Toda operator which was conjectured by the first and third authors. This form…
Non-Stationary Ruijsenaars Functions for and Intertwining Operators of Ding-Iohara-Miki Algebra
Masayuki Fukuda, Yusuke Ohkubo, Jun'ichi Shiraishi
We construct the non-stationary Ruijsenaars functions (affine analogue of the Macdonald functions) in the special case , using the intertwining operators of the Ding-Io…
Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
Masayuki Fukuda, Yusuke Ohkubo, Jun'ichi Shiraishi
An explicit formula is obtained for the generalized Macdonald functions on the -fold Fock tensor spaces, calculating a certain matrix element of a composition of several screene…
Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra
Yusuke Ohkubo
In this paper, we obtain the formula for the Kac determinant of the algebra arising from the level representation of the Ding-Iohara-Miki algebra. It is also discovered that it…
Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture
Yusuke Ohkubo
In this thesis, we obtain the formula for the Kac determinant of the algebra arising from the level representation of the Ding-Iohara-Miki algebra. This formula can be proved b…
(q,t)-KZ equation for Ding-Iohara-Miki algebra
Hidetoshi Awata, Hiroaki Kanno, Andrei Mironov +4
We derive the generalization of the Knizhnik-Zamolodchikov equation (KZE) associated with the Ding-Iohara-Miki (DIM) algebra U_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_1). We demons…
Anomaly in RTT relation for DIM algebra and network matrix models
H. Awata, H. Kanno, A. Mironov +4
We discuss the recent proposal of arXiv:1608.05351 about generalization of the RTT relation to network matrix models. We show that the RTT relation in these models is modified by a…
Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
Hidetoshi Awata, Hiroaki Kanno, Andrei Mironov +4
R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through t…
Explicit examples of DIM constraints for network matrix models
Hidetoshi Awata, Hiroaki Kanno, Takuya Matsumoto +5
Dotsenko-Fateev and Chern-Simons matrix models, which describe Nekrasov functions for SYM theories in different dimensions, are all incorporated into network matrix models with the…
Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
Yusuke Ohkubo, Hidetoshi Awata, Hiroki Fujino
In this paper, we consider the limit of the deformed Virasoro algebra and that of the level 1, 2 representation of Ding-Iohara-Miki algebra. Moreover, 5D AGT corr…
Existence and Orthogonality of Generalized Jack Polynomials and Its -Deformation
Yusuke Ohkubo
We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by def…