Brauer代数的中心维数问题

Brauer代数B_n(t)是一种在表示论,数学物理中重要的带一个参数t的有限维代数.当t取普通值时它们的结构已经了解得比较清楚,例如,不可约表示分类.当t取某些特殊值时有关它们还仍有些问题未探明.本文讨论任意参数时Brauer代数的中心的维数问题.主要结论是当t取某些特殊值时,Brauer代数中心的维数必定大于或等于t取普通值时它们的维数.

The Dimension of the Center of Brauer Algebra

Brauer algebra Bn(t) is a finite dimensional algebra with one parameter t which is important in representation theory and mathematical physics.For generic t , the structure of these algebras have been well understood, for example, their irreducible representations are classified.But for special t , many problem about their structure are still unclear.In this paper we discuss the dimension of the center of Brauer algebra for any parameter t.The main theorem is that for special t, the dimension of the center of Bn(t) is bigger than or equal the dimension of the center of Bn(t) when t is generic.