Hold Date

2021-07-01 16:00〜2021-07-01 18:00

Place

Zoom

Object person

　

Speaker

Ryosuke Nakahama (IMI Kyushu University, JSPS-PD)

Let $D\subset M(r,\mathbb{C})$ be the bounded symmetric domain, and we consider the weighted Bergman space $\mathcal{H}_\lambda(D)$ on $D$. Then $U(r,r)$ acts unitarily on $\mathcal{H}_\lambda(D)$. In this talk, we compute explicitly the inner products for some polynomials on $M(r',\mathbb{C})\oplus M(r'',\mathbb{C})$, $\operatorname{Alt}(r,\mathbb{C})$, $\operatorname{Sym}(r,\mathbb{C})\subset M(r,\mathbb{C})$, and prove that the inner products are given by multivariate hypergeometric polynomials when the polynomials are some powers of the determinants or the Pfaffians. As an application, we present the results on the construction of symmetry breaking operators from $U(r,r)$ to $U(r',r'')\times U(r'',r')$, $Sp(r,\mathbb{R})$ or $SO^*(2r)$.