Related papers: Character sheaves for classical symmetric pairs
The main theme of this paper is establishing the "generalized Springer correspondence" in complete generality that is, for not necessarily connected reductive algebraic groups.
In this paper, we study the classical theory of quadratic line complexes and Kummer surfaces. A quadratic line complex is the intersection of the Grassmannian $G(2,4)$ and a quadric hypersurface in ${\bf P}^5$, and a Kummer surface is the…
The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry. More recently, this theory has been fruitfully extended to…
We give an elementary proof of a theorem that characterizes quasisymmetric maps of the unit circle in terms of shear coordinates on the Farey tesselation. The proof only uses the normal family argument for quasisymmetric maps and some…
The appearance of quantum groups in conformal field theories is traced back to the Poisson-Lie symmetries of the classical chiral theory. A geometric quantization of the classical theory deforms the Poisson-Lie symmetries to the quantum…
Some connections between classical and nonclassical symmetries of a partial differential equation (PDE) are given in terms of determining equations of the two symmetries. These connections provide additional information for determining…
We discuss various computational issues around the problem of determining the character values of finite Chevalley groups, in the framework provided by Lusztig's theory of character sheaves. Some of the remaining open questions (concerning…
We develop a theory of sheaves and cohomology on the category of proper modulus pairs. This complements [KMSY21], where a theory of sheaves and cohomology on the category of non-proper modulus pairs has been developed.
This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…
We show relation between sign of Gaussian curvature of cuspidal edge and geometric invariants through types of singularities of Gauss map. Moreover, we define and characterize positivity/negativity of cusps of Gauss maps by geometric…
For Weyl groups of classical types, we present formulas to calculate the restriction of Springer representations to a maximal parabolic subgroup of the same type. As a result, we give recursive formulas for Euler characteristics of Springer…
We introduce an axiomatic theory of spherical diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context of Art Gallery problems for polyhedra and other…
A standard monomial theory for Schubert varieties is constructed exploiting (1) the geometry of the Seshadri stratifications of Schubert varieties by their Schubert subvarieties and (2) the combinatorial LS-path character formula for…
In this paper we introduce a certain class of families of Hessenberg varieties arising from Springer theory for symmetric spaces. We study the geometry of those Hessenberg varieties and investigate their monodromy representations in detail…
If $\lambda$ and $\mu$ are two non-empty Young diagrams with the same number of squares, and $\boldsymbol\lambda$ and $\boldsymbol\mu$ are obtained by dividing each square into $d^2$ congruent squares, then the corresponding character value…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
We analyze the onset of classical field configurations after a phase transition. Firstly, we motivate the problem by means of a toy model in quantum mechanics. Subsequently, we consider a scalar field theory in which the system-field…
The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
We prove invariance results for the cohomology groups of ideal sheaves of simple normal crossing divisors under (a restricted class of) birational morphisms of pairs in arbitrary characteristic, assuming a conjecture regarding the existence…