»ã±¨±êÌâ (Title)£ºHowe duality and invariant theory of i-quantum groups of type AIII (Howe¶ÔżÓëAIIIÐÍi-Á¿×ÓȺµÄ²»±äÁ¿ÀíÂÛ)

»ã±¨ÈË (Speaker)£ºÂÞÀõ ½ÌÊÚ (»ª¶«Ê¦·¶´óѧ)

»ã±¨¹¦·ò (Time)£º2023Äê11ÔÂ7ÈÕ(Öܶþ) 13:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿D121

Ô¼ÇëÈË(Inviter)£ººÎº£°²

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»ã±¨ÌáÒª£ºIt is known that for classical groups, the Schur duality, the Howe duality and the fundamental theorems of invariant theory are equivalent, though they are not equally straightforward. The same picture was not completed for quantum analogues except the general linear quantum groups, whose Schur duality, Howe duality and fundamental theorems of invariant theory was established by Jimbo, Zhang and Lehrer-Zhang-Zhang, respectively. In this talk, we shall provide the Howe duality and the fundamental theorems of invariant theory for the i-quantum groups of type AIII, which can be regarded as the case of quantum type B in the sense of Hecke algebras. This is joint work with Zheming Xu.