4,570 research outputs found
Generalized Preservation Principle in Finite Theta Correspondence
It is known that irreducible cuspidal characters satisfy the preservation
principle in the Howe correspondences of finite reductive dual pairs. In this
article, we generalize the preservation principle to any irreducible characters
of classical groups.Comment: The results in this paper replace Section 8-10 of old version of
arXiv:1906.0115
Finite Theta Correspondence of Almost Characters
The theory of almost characters which is closely related to character sheaves
is proposed by Lusztig to study the representation theory of finite reductive
groups. In this article we show that the decomposition of the Weil character
for finite reductive dual pairs (\Sp_{2n},\rmO^\pm_{2n'}) or
(\Sp_{2n},\SO_{2n'+1}) with respect to the almost characters is exactly the
same as the decomposition with respect to the irreducible characters. As a
consequence, the finite theta correspondence on almost characters is
established.Comment: 39 page
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