On the combinatorics of unramified admissible modules

On local newforms for unramified U(2,1)

Let G be the unramified unitary group in three variables defined over a p-adic field F of odd residual characteristic. In this paper, we investigate local newforms for irreducible admissible representations of G. We introduce a family of open compact subgroups {K_n} of G to define the local newforms for representations of G as the K_n-fixed vectors. We prove the existence of local newforms for generic representations and the multiplicity one property of the local newforms for admissible representations.

极大非分歧域扩张上的波前集

The wavefront set over a maximal unramified field extension

本文针对分裂于非分歧扩张的p-进约化群的深度0容许光滑复表示，发展了极大非分歧域扩张上波前集的研究理论，并将其用于计算球面Arthur表示的几何波前集，揭示了其与朗兰兹对偶群上反常层的关联。

On Representations of Reductive $p$--adic Groups over $\mathbb Q$--algebras

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some fundamental results in these settings, and as an example we give a classification of admissible unramified irreducible representations proving by reduction to the complex case that if the space of $K$--invariants is finite dimensional in an irreducible smooth unramified representation that the representation is admissible.

有限长度的无分歧GL₂

Finite length for unramified $\mathrm{GL}_2$

本文证明了在模p同调的Hecke特征空间中，GL₂(K)的可接受光滑表示具有有限长度，并探讨了这些表示的结构特性。

Admissible Diagrams in U_{q}^{w}(g) and Combinatoric Properties of Weyl Groups

Consider a complex simple Lie algebra g of rank n. Denote by Πa system of simple roots, by W the corresponding Weyl group, consider a reduced expression w = s_{α_{1}} ... s_{α_{t}} (each α_{i} in Π) of some w \in W and call diagram any subset of {1, ..., t}. We denote by U_{q}^{w}(g) the "quantum nilpotent" algebra defined by J. C. Jantzen. We prove (theorem 5.3. 1) that the positive diagrams naturally associated with the positive subexpressions (of the reduced expression of w) in the sense of R. Marsh and K. Rietsch, coincide with the admissible diagrams constructed by G. Cauchon which descri…

特征 $p$ 中 $p$-进 $\mathrm{GL}_{n}$ 的不可容许不可约表示

Non-admissible irreducible representations of $p$-adic $\mathrm{GL}_{n}$ in characteristic $p$

本文构造了特征 $p$ 中 $p$-进 $\mathrm{GL}_{n}$ 的光滑绝对不可约且不可容许的表示，推广了先前结果，并利用 Breuil-Paskunas 图表理论及抛物诱导。