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Intersections of Deligne--Lusztig varieties and Springer fibres
Zhe Chen
In this paper we prove a direct geometric relation between Deligne--Lusztig varieties and Springer fibres in type : For any rational unipotent element, the Springer fib…
Twisting operators and centralisers of Lie type groups over local rings
Zhe Chen
We extend the classical result asserting that the twisting operator preserves certain Deligne--Lusztig character values for truncated formal power series; along the way we discuss…
Flags and orbits of connected reductive groups over local rings
Zhe Chen
We prove that generic higher Deligne-Lusztig representations over truncated formal power series are non-nilpotent, when the parameters are non-trivial on the biggest reduction kern…
A note on cusp forms and representations of
Zhe Chen
Cusp forms are certain holomorphic functions defined on the upper half-plane, and the space of cusp forms for the principal congruence subgroup , a prime, is acted by $\m…
Green functions and higher Deligne--Lusztig characters
Zhe Chen
We give a generalisation of the character formula of Deligne--Lusztig representations from the finite field case to the truncated formal power series case. Motivated by this genera…
On the inner products of some Deligne--Lusztig type representations
Zhe Chen
In this paper we introduce a family of Deligne--Lusztig type varieties attached to connected reductive groups over quotients of discrete valuation rings, naturally generalising the…