Howe correspondence between Harish-Chandra series
Time: Mon, 13 May 2019, 13:30-15:05
Place: Lecture hall, Jinchunyuan west building, Tsinghua University
Speaker: Jesua Epequin (AMSS)
Abstract:
Let 𝔽q be a finite field with q elements and odd characteristic. A pair (G, G′) of mutually centralized reductive subgroups of Sp2n(𝔽q) is called a reductive dual pair. By means of the Weil representation of Sp2n(𝔽q), Roger Howe introduced a correspondence Θ: ℛ(G) → ℛ(G′) between the category of complex representations of these subgroups. Here we discuss how this correspondence relates the Harish-Chandra series of G to those of G′. If time allows, we will discuss how this correspondance can be expressed as a correspondance between unipotent Harish-Chandra series.