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過去の記録 ～04/25｜次回の予定｜今後の予定 04/26～
| 開催情報 | 土曜日 13:30～16:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 神保道夫、国場敦夫、山田裕二、武部尚志、高木太一郎、白石潤一 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~takebe/iat/index-j.html |
2011年10月22日(土)
13:30-16:00 数理科学研究科棟(駒場) 117号室
Leonid Rybnikov 氏 (IITP, and State University Higher School of Economics,
Department of Mathematics) 13:30-14:30
Quantization of Quasimaps' Spaces (joint work with M. Finkelberg) (ENGLISH)
Instituteof Biochemical Physics) 15:00-16:00
Quantum integrable models with elliptic R-matrices
and elliptic hypergeometric series (ENGLISH)
Leonid Rybnikov 氏 (IITP, and State University Higher School of Economics,
Department of Mathematics) 13:30-14:30
Quantization of Quasimaps' Spaces (joint work with M. Finkelberg) (ENGLISH)
[ 講演概要 ]
Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a
remarkable compactification of the space of based degree d maps from
the projective line to the flag variety of type A. The space Z_d has a
natural Poisson structure,
which goes back to Atiyah and Hitchin. We describe
the Quasimaps' space as some quiver variety, and define the
Atiyah-Hitchin Poisson structure in quiver terms.
This gives a natural way to quantize this Poisson structure.
The quantization of the coordinate ring of the Quasimaps' space turns
to be some natural subquotient of the Yangian of type A.
I will also discuss some generalization of this result to the BCD types.
Anton Zabrodin 氏 ( Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a
remarkable compactification of the space of based degree d maps from
the projective line to the flag variety of type A. The space Z_d has a
natural Poisson structure,
which goes back to Atiyah and Hitchin. We describe
the Quasimaps' space as some quiver variety, and define the
Atiyah-Hitchin Poisson structure in quiver terms.
This gives a natural way to quantize this Poisson structure.
The quantization of the coordinate ring of the Quasimaps' space turns
to be some natural subquotient of the Yangian of type A.
I will also discuss some generalization of this result to the BCD types.
Instituteof Biochemical Physics) 15:00-16:00
Quantum integrable models with elliptic R-matrices
and elliptic hypergeometric series (ENGLISH)
[ 講演概要 ]
Intertwining operators for infinite-dimensional representations of the
Sklyanin algebra with spins l and -l-1 are constructed using the technique of
intertwining vectors for elliptic L-operator. They are expressed in
terms of
elliptic hypergeometric series with operator argument. The intertwining
operators obtained (W-operators) serve as building blocks for the
elliptic R-matrix
which intertwines tensor product of two L-operators taken in
infinite-dimensional
representations of the Sklyanin algebra with arbitrary spin. The
Yang-Baxter equation
for this R-matrix follows from simpler equations of the star-triangle
type for the
W-operators. A natural graphic representation of the objects and
equations involved
in the construction is used.
Intertwining operators for infinite-dimensional representations of the
Sklyanin algebra with spins l and -l-1 are constructed using the technique of
intertwining vectors for elliptic L-operator. They are expressed in
terms of
elliptic hypergeometric series with operator argument. The intertwining
operators obtained (W-operators) serve as building blocks for the
elliptic R-matrix
which intertwines tensor product of two L-operators taken in
infinite-dimensional
representations of the Sklyanin algebra with arbitrary spin. The
Yang-Baxter equation
for this R-matrix follows from simpler equations of the star-triangle
type for the
W-operators. A natural graphic representation of the objects and
equations involved
in the construction is used.
