Related papers: Commutative character sheaves and geometric types …

Let $\mathtt{k}$ be an algebraic closure of a finite field $\mathbb{F}_{q}$ of characteristic $p$. Let $G$ be a connected unipotent group over $\mathtt{k}$ equipped with an $\mathbb{F}_q$-structure given by a Frobenius map $F:G\to G$. We…

The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example,…

Let $F$ be a non-Archimedean local field with odd characteristic $p$. Let $N$ be a positive integer and $G=Sp_{2N}(F)$. By work of Lomel\'i on $\gamma$-factors of pairs and converse theorems, a generic supercuspidal representation $\pi$ of…

Let H be a connected reductive group over an algebraically closed field. We define a surjective map from the set CS(H) of unipotent character sheaves on H (up to isomorphism) to the set of strata of H. To do this we use the generalized…

We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of…

Given a $p$-adic group $G=\mathbf{G}(F)$ and a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$ such that the fixed-point subgroup $\mathbf{G}^\Gamma$ is reductive, we show that every semisimple character (in the sense of Bushnell and…

We study the intermediate extension of the character sheaves on an adjoint group to the semi-stable locus of its wonderful compactification. We show that the intermediate extension can be described by a direct image construction. As a…

Let $\text{E}/\text{F}$ be a quadratic extension of non-Archimedean local fields with odd residual characteristic. In this paper, we give equivalent conditions for a simple supercuspidal representation $\pi$ of $\text{GL}(n, \text{E})$ to…

We re-write the character formul{\ae} of Adler and the second-named author in a form amenable to explicit computations in $p$-adic harmonic analysis, and use them to prove the stability of character sums for a modification of Reeder's…

Let $F$ be a finite extension of ${\mathbb{Q}} \_p$. Any dihedral supercuspidal representation of $GL \_2 (K)$ arises from an admissible multiplicative character $\omega$ of a quadratic extension $L$ of $K$. We show that such a…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

Let $G$ be a finite Chevalley group. We are concerned with computing the values of the unipotent characters of $G$ by making use of Lusztig's theory of character sheaves. In this framework, one has to find the transformation between several…

Six-dimensional N=(1,0) superconformal field theories can be engineered geometrically via F-theory on elliptically-fibered Calabi-Yau 3-folds. We include torsional sections in the geometry, which lead to a finite Mordell-Weil group. This…

We compute quantum character varieties of arbitrary closed surfaces with boundaries and marked points. These are categorical invariants $\int_S\mathcal A$ of a surface $S$, determined by the choice of a braided tensor category $\mathcal A$,…

We propose a definition of characters in the context of Schneider-Teitelbaum's theory of locally analytic representations of p-adic reductive groups. This character will be a function on a compact subgroup of a maximal torus of the…

In this paper, we introduce Topological Quantum Field Theories (TQFTs) generalizing the arithmetic computations done by Hausel and Rodr\'iguez-Villegas and the geometric construction done by Logares, Mu\~noz, and Newstead to study…

Let $F$ be a non-Archimedean local field, with the ring of integers $\mathfrak{o}_F. Let $G=GL_N(F)$, $K=GL_N(\mathfrak{o}_F)$ and $\pi$ a supercuspidal representation of $G$. We show that there exist a unique irreducible smooth…

We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry…

Let $E/F$ be a unramified quadratic extension of non-archimedean local fields of odd characteristic $p$, and $G$ be the unramified unitary group $U(2, 1)(E/F)$. For an irreducible smooth representation $\pi$ of $G$ over…

In this work, we set up a theory of p-adic modular forms over Shimura curves over totally real fields which allows us to consider also non-integral weights. In particular, we define an analogue of the sheaves of k-th invariant differentials…