[[back to conference page>ochiai/pv]] - Hideyuki Ishi --Analysis on regular convex cones associated to decomposable graphs --Regular convex cones of positive definite real symmetric matrices with prescribed zero entries have been studied intensively in multivariate statistics. It turned out that analysis on the cone is quite feasible if the zero pattern corresponds to a decomposable graph. Indeed, an explicit formula is known for the Fourier-Laplace transform of a product of powers of minors over the cone. Inspired by these statistic works, we develop analysis on the cone in a similar way to theory of homogeneous cones. In particular, we consider Riesz distributions on the cone and associated b-functions. -Yumiko Hironaka --Spherical functions on certain $p$-adic homogeneous spaces, and some relation to PV-theory --First I want to introduce a typical spherical function on certain homogeneous space $X$, and give its expression formula by using functional equations of sph. f's and data of the group. In this talk everything is assumed to be defined over a $\mathfrak{p}$-adic field $k$. Typical sph. f's are obtained by Poisson transform from relative $P$-invariant on $X$, where $P$ is a minimal parabolic that has Zarisky open orbit in $X$ over $\overline{k}$, and their functional equations are often reduced to those for certain limited type of prehomogeneous vector spaces. Then I want to discuss about some spaces of sesquiliear forms, and give explicit formulas of sph.f's by using specialized Hall-Littlewood polynomials associated to the root system, parametrization of all the sph.f's, and Plancherel formula. (The latter half is joint work with Y. Komori.)