有限射影幾何の組合せ構造の代数的性質について

Tohoku University田中太初課

Terwilliger algebras of generalized wreath products of association schemes

The generalized wreath product of association schemes was introduced by R.~A.~Bailey in European Journal of Combinatorics 27 (2006) 428--435. It is known as a generalization of both wreath and direct products of association schemes. In this paper, we discuss the Terwilliger algebra of the generalized wreath product of commutative association schemes. I will describe its structure and its central primitive idempotents in terms of the parameters of each factors and their central primitive idempotents.Comment: 17 page

Nadel type, Bogomolov-Sommese type vanishing and singular dual Nakano semi-positivity

In this article, we get properties for singular (dual) Nakano semi-positivity and obtain singular type vanishing theorem involving $L^2$-subsheaves on weakly pseudoconvex manifolds by $L^2$-estimates and $L^2$-type Dolbeault isomorphism. As applications, the Fujita Conjecture type theorem with singular Hermitian metrics is presented.Comment: 43page