相关论文: $\mathfrak{G}$-Quotients of Grassmannians and Equa…

Let $\mathbb{K}$ be the algebraic closure of a finite field $\mathbb{F}_q$ of odd characteristic $p$. For a positive integer $m$ prime to $p$, let $F=\mathbb{K}(x,y)$ be the transcendency degree $1$ function field defined by…

The subgroup K=GL_p x GL_q of GL_{p+q} acts on the (complex) flag variety GL_{p+q}/B with finitely many orbits. We introduce a family of polynomials that specializes to representatives for cohomology classes of the orbit closures in the…

We study a family of (possibly non topological) deformations of $BF$ theory for the Lie algebra obtained by quadratic extension of $\mathfrak{so}(3,1)$ by an orthogonal module. The resulting theory, called quadratically extended General…

The literature on maximal torus orbits in the Grassmannian is vast; in this paper we initiate a program to extend this to diagonal subtori. Our main focus is generalizing portions of Kapranov's seminal work on Chow quotient…

Let $X$ be a complex $K3$ surface with an effective action of a group $G$ which preserves the holomorphic symplectic form. Let $$ Z_{X,G}(q) = \sum_{n=0}^{\infty} e\left(\operatorname{Hilb}^{n}(X)^{G} \right)\, q^{n-1} $$ be the generating…

We state a conjecture, local Langlands in families, connecting the centre of the category of smooth representations on $\mathbb{Z}[\sqrt{q}^{-1}]$-modules of a quasi-split $p$-adic group $\mathrm{G}$ (where $q$ is the cardinality of the…

This work reports on joint research with Manuel Saorin. For an algebra A over an algebraically closed field k the set of A-module structures on k d forms an affine algebraic variety. The general linear group Gl d (k) acts on this variety…

The notion of a continuous $G$-action on a topological space readily generalizes to that of a continuous $D$-action, where $D$ is any small category. Dror Farjoun and Zabrodsky introduced a generalized notion of orbit, which is key to…

Consider a standard representation $\pi_{st}$ of a quasi-split reductive p-adic group G. The generalized injectivity conjecture, posed by Casselman and Shahidi, asserts that any generic irreducible subquotient $\pi$ of $\pi_{st}$ is…

We introduce a family of algebras $\mathcal{A}_{M,N}$, $M,N\in\mathbb{Z}$, as an extension of a pair of commuting quantum toroidal $\mathfrak{gl}_1$ subalgebras $\mathcal{E}_1,\check{\mathcal{E}}_1$, wherein the parameters are tuned in a…

Let $G$ be a classical group of dimension $d$ and let $\boldsymbol{a}=(a_1,\dots,a_d)$ be differential indeterminates over a differential field $F$ of characteristic zero with algebraically closed field of constants $C$. Further let…

We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality of a finite field F, we obtain an isomorphism with the derived Hall…

Let $G$ be a connected reductive algebraic group defined over the finite field $\F_q$, where $q$ is a power of a good prime for $G$, and let $F$ denote the corresponding Frobenius endomorphism, so that $G^F$ is a finite reductive group. Let…

We consider the algebra $\mathcal O(\mathsf M)$ of observables and the (formally) versal morphism $\eta: A \to \mathcal O(\mathsf M)$ defined by the noncommutative deformation functor $\mathsf{Def}_{\mathsf M}$ of a family $\mathsf M = \{…

Let $\Gamma$ be a discrete finitely generated group. Let $\hat{M}\to T$ be a $\Gamma$-equivariant fibration, with fibers diffeomorphic to a fixed even dimensional manifold with boundary $Z$. We assume that $\Gamma\to \hat{M}\to…

For a simple linear algebraic group $G$, the chiral universal centralizer $\mathbf{I}_{G,k}$ is a vertex operator algebra, which is the chiralization of the universal centralizer $\mathfrak{Z}_G$. The variety $\mathfrak{Z}_G$ is identified…

Let $\Bbbk$ be an algebraically closed field, $Q$ a finite quiver, and denote by $\mathop{\mathrm{rep}}_Q^{\mathbf{d}}$ the affine $\Bbbk$-scheme of representations of $Q$ with a fixed dimension vector ${\mathbf{d}}$. Given a representation…

Let $\mathbf{LG}(V\oplus V^*)$ and $\mathbf{OG}^+(V\oplus V^*)$ denote the Lagrangian and orthogonal Grassmannians endowed with the natural $\mathbb{G}_m$-actions, respectively. Thaddeus proved that over $\mathbb{C}$, the Hilbert quotients…

Let G be a reductive linear algebraic group, H a reductive subgroup of G and X an affine G-variety. Let Y denote the set of fixed points of H in X, and N(H) the normalizer of H in G. In this paper we study the natural map from the quotient…

If $X'= ({\mathbb B} / \Gamma)'$ is a torsion free toroidal compactification of a discrete ball quotient $X_o={\mathbb B} / \Gamma$ and $\xi : (X', T = X'\setminus X_o) \rightarrow (X, D = \xi (T))$ is the blow-down of the $(-1)$-curves to…