本文印刷
全画面プリント
Lie群論・表現論セミナー
過去の記録 ～06/28｜次回の予定｜今後の予定 06/29～
| 開催情報 | 火曜日 16:30～18:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 小林俊行 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html |
2015年01月27日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
大矢浩徳 氏 (東京大学大学院数理科学研究科)
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases (JAPANESE)
大矢浩徳 氏 (東京大学大学院数理科学研究科)
Representations of quantized function algebras and the transition matrices from Canonical bases to PBW bases (JAPANESE)
[ 講演概要 ]
Let G be a connected simply connected simple complex algebraic group of type ADE and g the corresponding simple Lie algebra. In this talk, I will explain our new algebraic proof of the positivity of the transition matrices from the canonical basis to the PBW bases of Uq(n+). Here, Uq(n+) denotes the positive part of the quantized enveloping algebra Uq(g). (This positivity, which is a generalization of Lusztig's result, was originally proved by Kato (Duke Math. J. 163 (2014)).) We use the relation between Uq(n+) and the specific irreducible representations of the quantized function algebra Qq[G]. This relation has recently been pointed out by Kuniba, Okado and Yamada (SIGMA. 9 (2013)). Firstly, we study it taking into account the right Uq(g)-algebra structure of Qq[G]. Next, we calculate the transition matrices from the canonical basis to the PBW bases using the result obtained in the first step.
Let G be a connected simply connected simple complex algebraic group of type ADE and g the corresponding simple Lie algebra. In this talk, I will explain our new algebraic proof of the positivity of the transition matrices from the canonical basis to the PBW bases of Uq(n+). Here, Uq(n+) denotes the positive part of the quantized enveloping algebra Uq(g). (This positivity, which is a generalization of Lusztig's result, was originally proved by Kato (Duke Math. J. 163 (2014)).) We use the relation between Uq(n+) and the specific irreducible representations of the quantized function algebra Qq[G]. This relation has recently been pointed out by Kuniba, Okado and Yamada (SIGMA. 9 (2013)). Firstly, we study it taking into account the right Uq(g)-algebra structure of Qq[G]. Next, we calculate the transition matrices from the canonical basis to the PBW bases using the result obtained in the first step.
