Related papers: The Chow rings of the algebraic groups E_6, E_7, a…
This paper is the first in a series dedicated to computing the integral Chow rings of the moduli stacks of Prym pairs. In this work, we compute the Chow ring for Prym pairs arising from a single pair of Weierstrass points and from at most…
Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads to a characterization of the toroidal and horospherical partial flag varieties with Picard…
We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and…
While there is much work and many conjectures surrounding the intersection theory of the moduli space of curves, relatively little is known about the intersection theory of the Hurwitz space $\mathcal{H}_{k, g}$ parametrizing smooth degree…
Given a projective algebraic variety $X$, let $\Pi_p(X)$ denote the monoid of effective algebraic equivalence classes of effective algebraic cycles on $X$. The $p$-th Euler-Chow series of $X$ is an element in the formal monoid-ring…
Based on recent advances on the relation between geometry and representation theory, we propose a new approach to elliptic Schubert calculus. We study the equivariant elliptic characteristic classes of Schubert varieties of the generalized…
We present a categorification of four mutation finite cluster algebras by the cluster category of the category of coherent sheaves over a weighted projective line of tubular weight type. Each of these cluster algebras which we call tubular…
A result of A. King and C. Walter asserts that the Chow ring of a fine quiver moduli space is generated by the Chern classes of universal bundles if the quiver is acyclic. We will show that defining relations between these Chern classes…
Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by Moeglin and for the exceptional Chevalley group G_2 by…
When considering the unit group of $\mathcal{O}_F G$ ($\mathcal{O}_F$ the ring of integers of an abelian number field $F$ and a finite group $G$) certain components in the Wedderburn decomposition of $FG$ cause problems for known generic…
We use an Euler system of Heegner cycles to bound the Selmer group associated to a modular form of higher even weight twisted by a ring class character. This is an extension of Nekovar's result that uses Bertolini and Darmon's refinement of…
This paper aims to focus on Richardson varieties on symplectic groups, especially their combinatorial characterization and defining equations. Schubert varieties and opposite Schubert varieties have profound significance in the study of…
We give the formula for multiplying a Schubert class on an odd orthogonal or symplectic flag manifold by a special Schubert class pulled back from a Grassmannian of maximal isotropic subspaces. This is also the formula for multiplying a…
The five exceptional simple Lie algebras over the complex number are included one within the other as $G_2 \subset F_4 \subset E_6 \subset E_7 \subset E_8$. The biggest one, $E_8$, is in many ways the most mysterious. This article surveys…
We discuss Jacobi forms that are invariant under the action of the Weyl group of type E_n (n=6,7,8). For n=6,7 we explicitly construct a full set of generators of the algebra of E_n weak Jacobi forms. We first construct n+1 independent E_n…
For an algebraically closed field K with ch K \not = 2, we determine the Chow ring of the moduli space of holomorphic bundles on a projective plane with the structure group SO(n,K) and half the first Pontryagin index being equal to 1, each…
In these notes, we survey the homology of the loop group Omega(K) of a compact group K, also known as the affine Grassmannian of a complex loop group. Using the Bott picture of H_*(Omega(K)), the homology algebra or Pontryagin ring, we…
Similarly to how the classical group ring isomorphism problem asks, for a commutative ring $R$, which information about a finite group $G$ is encoded in the group ring $RG$, the twisted group ring isomorphism problem asks which information…
For each minuscule flag variety $X$, there is a corresponding minuscule poset, describing its Schubert decomposition. We study an action on plane partitions over such posets, introduced by P. Cameron and D. Fon-der-Flaass (1995). For plane…
We continue the study of twisted automorphisms of Hopf algebras started in "Twisted automorphisms of Hopf algebras". In this paper we concentrate on the group algebra case. We describe the group of twisted automorphisms of the group algebra…