Related papers: On global Schubert varieties for the general linea…
We introduce a global equivariant refinement of algebraic K-theory; here `global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global…
Let mathcal{O}_lambda be a generic coadjoint orbit of a compact semi-simple Lie group K. Weight varieties are the symplectic reductions of mathcal{O}_lambda by the maximal torus T in K. We use a theorem of Tolman and Weitsman to compute the…
The goal of the paper is twofold: on one side it provides an order structure on the set of all maximal chains in the Bruhat poset of Schubert varieties in a Grassmann variety; on the other hand, using this order structure, it works out…
We study the multiplicity number of the characteristic cycle of the intersection complex of the matroid Schubert variety. It is shown to be a combinatorial invariant, and it can be computed by explicit formulas. We also conjecture that the…
In earlier papers it was shown that the generic tropical variety of an ideal can contain information on algebraic invariants as for example the depth in a direct way. The existence of generic tropical varieties has so far been proved in the…
Let X = G/P be a cominuscule rational homogeneous variety. (Equivalently, X admits the structure of a compact Hermitian symmetric space.) I give a uniform description (that is, independent of type) of the irreducible components of the…
Let $G$ be a simply connected, almost simple group over an algebraically closed field $\mathbf k$, and $P$ a maximal parabolic subgroup corresponding to omitting a cominuscule root. We construct a compactification $\phi:T^*G/P\rightarrow…
We prove that for every complex classical group $G$ the string polytope associated to a special reduced decomposition and any dominant integral weight $\lambda$ will be a lattice polytope if and only if the highest weight representation of…
A lattice model for four dimensional Euclidean quantum general relativity is proposed for a simplicial spacetime. It is shown how this model can be expressed in terms of a sum over worldsheets of spin networks, and an interpretation of…
We propose a geometric interpretation of the classical Rankin-Selberg method for GL(n) in the framework of the geometric Langlands program. We show that the geometric Langlands conjecture for an irreducible unramified local system $E$ of…
In order to extend the geometrization of Yangian $R$-matrices from Lie algebras $gl(n)$ to superalgebras $gl(M|N)$, we introduce new quiver-related varieties which are associated with representations of $gl(M|N)$. In order to define them…
In this paper, we propose an algebraic approach via Lakshmibai-Seshadri (LS) algebras to establish a link between standard monomial theories, Newton-Okounkov bodies and valuations. This is applied to Schubert varieties, where this approach…
We construct, for any finite commutative ring $R$, a family of representations of the general linear group $\mathrm{GL}_n(R)$ whose intertwining properties mirror those of the principal series for $\mathrm{GL}_n$ over a finite field.
We classify all triples $(G,V,H)$ such that $SL_n(q)\leq G\leq GL_n(q)$, $V$ is a representation of $G$ of dimension greater than one over an algebraically closed field $\FF$ of characteristic coprime to $q$, and $H$ is a proper subgroup of…
We consider abelian gauge theories on a lattice and develop properties of an axial gauge that is covariant under lattice symmetries. Particular attention is paid to a version that behaves nicely under block averaging renormalization group…
We compute the universal weight system for Vassiliev invariants coming from the Lie superalgebra gl(1|1) applying the construction of \cite{YB}. This weight system is a function from the space of chord diagrams to the center $Z$ of the…
We study the Steinberg lattice of the general linear group when reduced modulo a prime different from the defining characteristic.
We introduce the notion of a cominuscule point in a Schubert variety in a generalized flag variety for a semisimple group. We derive formulas expressing the Hilbert series and multiplicity of a Schubert variety at a cominuscule point in…
In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on…
New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation…