$q$-deformed orthosymplectic Howe duality
배정
129동 406호
0
1034
2025.08.19 18:32
| 구분 | 박사학위 논문 발표 |
|---|---|
| 일정 | 2025-09-09(화) 16:00~17:00 |
| 세미나실 | 129동 406호 |
| 강연자 | 배정 (서울대학교) |
| 담당교수 | 권재훈 |
| 기타 |
There is a well-known duality between a Lie group $G$ and a Lie superalgebra $\mathfrak{g}$ on a supersymmetric algebra, which is called Howe duality. We give a $q$-analogue of the orthosymplectic Howe duality associated to the orthogonal or symplectic Lie group $G=O_\ell$ or $Sp_{2\ell}$ and orthosymplectic Lie superalgebra $\mathfrak{g} = \mathfrak{osp}_X(\epsilon)$. As a $q$-deformation of $\mathfrak{g}$, we use generalized quantum group of type D and C. As a $q$-deformation of $G$, we use $\imath$quantum group corresponding to the symmetric pairs of type AI $(\mathfrak{sl}_\ell, \mathfrak{so}_\ell)$ and AII $(\mathfrak{sl}_{2\ell}, \mathfrak{sp}_{2\ell})$.
In particular, we define explicit actions of the generalized quantum group and the $\imath$quantum group on a $q$-deformed supersymmetric algebra. Then we verify the commutativity of those two actions by direct computation. We further present a semisimple decomposition of a $q$-deformed supersymmetric algebra, and show that the decomposition recovers the classical orthosymplectic Howe duality in the classical limit. 