9 citations · 26 across the 13 of their papers we have counts for
14 papers
Finiteness of planar central configurations of five bodies for all positive masses: On Smale's sixth problem
Zhe Chen, Zhicheng Tong
We prove that for every choice of five positive masses the planar five-body problem has only finitely many central configurations up to rotation, translation and scaling. This answ…
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…
Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras
Zhe Chen, Ian Marquette, Yao-Zhong Zhang
We present a new method for constructing -dimensional minimally superintegrable systems based on block coordinate separation of variables. We give two new families of superinteg…
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…
Extended Laplace-Runge-Lentz vectors, new family of superintegrable systems and quadratic algebras
Zhe Chen, Ian Marquette, Yao-Zhong Zhang
We present a useful proposition for discovering extended Laplace-Runge-Lentz vectors of certain quantum mechanical systems. We propose a new family of superintegrable systems and c…
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…
Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes
Zhe Chen, Lasse Leskelä, Lauri Viitasaari
In this article we study the existence of pathwise Stieltjes integrals of the form for nonrandom, possibly discontinuous, evaluation functions and Hölder c…
The algebraisation of higher Deligne--Lusztig representations
Zhe Chen, Alexander Stasinski
In this paper we study higher Deligne--Lusztig representations of reductive groups over finite quotients of discrete valuation rings. At even levels, we show that these geometrical…
Generic character sheaves on reductive groups over a finite ring
Zhe Chen
In this paper we propose a construction of generic character sheaves on reductive groups over finite local rings at even levels, whose characteristic functions are higher Deligne--…
Aspects of Stochastic Integration with Respect to Processes of Unbounded p-variation
Zhe Chen, Lauri Viitasaari
This paper deals with stochastic integrals of form in a case where the function has discontinuities, and hence the process is usually of unbounded…
Pathwise stochastic integrals and Itô formula for multidimensional Gaussian processes
Zhe Chen, Lauri Viitasaari
In this article we study existence of pathwise stochastic integrals with respect to a general class of -dimensional Gaussian processes and a wide class of adapted integrands. Mo…