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Lie Groups and Representation Theory
Seminar information archive ～04/24｜Next seminar｜Future seminars 04/25～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|
2021/11/16
17:00-18:00 Room #on line (Graduate School of Math. Sci. Bldg.)
Ryosuke Nakahama (Kyushu University)
Computation of weighted Bergman norms on block diagonal matrices in bounded symmetric domains (Japanese)
Ryosuke Nakahama (Kyushu University)
Computation of weighted Bergman norms on block diagonal matrices in bounded symmetric domains (Japanese)
[ Abstract ]
Let $G/K\simeq D\subset\mathfrak{p}^+$ be a Hermitian symmetric space realized as a bounded symmetric domain, and we consider the weighted Bergman space $\mathcal{H}_\lambda(D)$ on $D$.
Then the norm on each $K$-type in $\mathcal{H}_\lambda(D)$ is explicitly computed by Faraut--Kor\'anyi (1990).
In this talk, we consider the cases $\mathfrak{p}^+=\operatorname{Sym}(r,\mathbb{C})$, $M(r,\mathbb{C})$, $\operatorname{Alt}(2r,\mathbb{C})$, fix $r=r'+r''$, and decompose $\mathfrak{p}^+$ into $2\times 2$ block matrices.
Then the speaker presents the results on explicit computation of the norm of $\mathcal{H}_\lambda(D)$ on each $K'$-type in the space of polynomials on the block diagonal matrices $\mathfrak{p}^+_{11}\oplus\mathfrak{p}^+_{22}$.
Also, as an application, the speaker presents the results on Plancherel-type formulas on the branching laws for symmetric pairs $(Sp(r,\mathbb{R}),U(r',r''))$, $(U(r,r),U(r',r'')\times U(r'',r'))$, $(SO^*(4r),U(2r',2r''))$.
Let $G/K\simeq D\subset\mathfrak{p}^+$ be a Hermitian symmetric space realized as a bounded symmetric domain, and we consider the weighted Bergman space $\mathcal{H}_\lambda(D)$ on $D$.
Then the norm on each $K$-type in $\mathcal{H}_\lambda(D)$ is explicitly computed by Faraut--Kor\'anyi (1990).
In this talk, we consider the cases $\mathfrak{p}^+=\operatorname{Sym}(r,\mathbb{C})$, $M(r,\mathbb{C})$, $\operatorname{Alt}(2r,\mathbb{C})$, fix $r=r'+r''$, and decompose $\mathfrak{p}^+$ into $2\times 2$ block matrices.
Then the speaker presents the results on explicit computation of the norm of $\mathcal{H}_\lambda(D)$ on each $K'$-type in the space of polynomials on the block diagonal matrices $\mathfrak{p}^+_{11}\oplus\mathfrak{p}^+_{22}$.
Also, as an application, the speaker presents the results on Plancherel-type formulas on the branching laws for symmetric pairs $(Sp(r,\mathbb{R}),U(r',r''))$, $(U(r,r),U(r',r'')\times U(r'',r'))$, $(SO^*(4r),U(2r',2r''))$.
