Euler characters and super Jacobi polynomials

Jacobi-Trudi type formula for character of irreducible representations of $\frak{gl}(m|1)$

We prove a determinantal type formula to compute the irreducible characters of the general Lie superalgebra $\mathfrak{gl}(m|1)$ in terms of the characters of the symmetric powers of the fundamental representation and their duals. This formula was conjectured by J. van der Jeugt and E. Moens for the Lie superalgebra $\frak{gl}(m|n)$ and generalizes the well-known Jacobi-Trudi formula.

Euler characteristics and compact p-adic Lie groups

We discuss Euler characteristics for finitely generated modules over Iwasawa algebras. We show that the Euler characteristic of a module is well-defined whenever the 0th homology group is finite if and only if the relevant compact p-adic Lie group is finite-by-nilpotent and that in this case all pseudo-null modules have trivial Euler characteristic. We also prove some other results relating to the triviality of Euler characteristics for pseudo-null modules. We also prove some analogous results for the Akashi series of Coates et al.

Jacobi-Trudi determinants and characters of minimal affinizations

In their study of characters of minimal affinizations of representations of orthogonal and symplectic Lie algebras, Chari and Greenstein conjectured that certain Jacobi-Trudi determinants satisfy an alternating sum formula. In this note, we prove their conjecture and slightly more. The proof relies on some symmetries of the ring of symmetric functions discovered by Koike and Terada. Using results of Hernandez, Mukhin-Young, and Naoi, this implies that the characters of minimal affinizations in types B, C, and D are given by a Jacobi-Trudi determinant.

特征展开与仿射Jacobi-Trudi恒等式

Character expansions and affine Jacobi-Trudi identities

本文通过给出B_n、C_n和BC_n型多参数Hall--Littlewood多项式在矩形形状下的特征展开，证明了Ole Warnaar提出的六个仿射Jacobi-Trudi型恒等式。

Remarks on modules of the ortho-symplectic Lie superalgebras

We examine in detail the Jacobi-Trudi characters over the ortho-symplectic Lie superalgebras spo(2|2m+1) and spo(2n|3). We furthermore relate them to Serganova's notion of Euler characters.