Zhi Chen

• Nanjing Agricultural University

This paper gives a plethysm formula on the characteristic map of the induced linear characters from the unipotent upper-triangular matrices Un(Fq) to GLn(Fq), the general linear group over finite field Fq. The result turns out to be a multiple of a twisted version of the Hall-Littlewood symmetric functions Pn[Y; q]. A recurrence relation is also gi...

We give a characterization of and a trace formula for trace class pseudo-differential operators on the unit sphere $\mathbb{S }^{n-1}$ centered at the origin in $\mathbb{R }^n$ .

International audience We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows d...

Given a list of $n$ cells $L=[(p_1,q_1),...,(p_n, q_n)]$ where $p_i, q_i\in \textbf{Z}_{\ge 0}$, we let $\Delta_L=\det |{(p_j!)^{-1}(q_j!)^{-1} x^{p_j}_iy^{q_j}_i} |$. The space of diagonally alternating polynomials is spanned by $\{\Delta_L\}$ where $L$ varies among all lists with $n$ cells. For $a>0$, the operators $E_a=\sum_{i=1}^{n} y_i\partial...

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to...

In this paper, we study the norm squares Bp for Qp spaces and norm squares Ap for Mp spaces on the unit ball of Cn. For a holomorphic function f on the unit ball, we prove thatBp(f)⩽∫01gp(t)dψ(t)∫01gq(t)dψ(t)⋅Bq(f) holds for (n−1)/nqpn/(n−1), whereg(t)=n+12n∫t1(1−τ2)n−1τ−2n+1dτ,ψ(t)=t2n(1−t2)n−1, and thatAp(f)⩽p(nq+1)B(n,n(p−1)+1)q(np+1)B(n,n(q−1)+...