第2回

日時

2019年5月10日(金) 17:30~19:00

場所

I-siteなんば 2F S1 (I-siteなんばへは，地下鉄御堂筋線大国町駅が最寄りです．)

講演者

渡邉英也氏(大阪大学)

タイトル

A new approach to classical representations of non-standard quantum group $U’_q(so_n)$

アブストラクト

Besides Drinfeld-Jimbo quantum group $U_q(so_n)$, there is another q-deformation $U’_q(so_n)$ of the special orthogonal Lie algebra. A remarkable feature of this non-standard quantum group is that it has the canonical chain $U’_q(so_3) \subset U’_q(so_4) \subset U’_q(so_5) \subset \cdots$. This enables one to study the finite-dimensional irreducible $U’_q(so_n)$-modules by means of an analog of Gelfand-Tsetlin bases. In this talk, I will propose a different approach to this subject. Namely, I will construct a new algebra which has some $sl_2$-triple like generators, and prove that a certain module category of this algebra is equivalent to the category of classical $U’_q(so_n)$-modules.