Related papers: Composition series for GKZ-systems
By using perverse sheaves on representation spaces of quivers over $k[t]/(t^n)$ and jet schemes over flag varieties, we construct a geometric composition algebra $\mathbf K$ under Lusztig's framework on geometric realizations of the…
We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twisted period relation, we obtain a formula of cohomology…
In this paper we construct $G$-Hilbert schemes for finite group schemes $G$. We find a construction of $G$-Hilbert schemes as relative $G$-Hilbert schemes over the quotient that does not need the Hilbert scheme of $n$ points, works under…
This is a survey paper on the Riemann-Hilbert correspondence on (irregular) holonomic D-modules, based on the 16-th Takagi lecture (2015/11/28). In this paper, we use subanalytic sheaves, an analogous notion to the one of indsheaves.
In the strict semi stable reduction situation, we describe the various filtrations of the perverse sheaf of nearby cycles in terms of irreducible perverse sheaves together with the action of the monodromy operator. We then study the…
We characterize strong continuity of general operator semigroups on some Lebesgue spaces. In particular, a characterization of strong continuity of weighted composition semigroups on classical Hardy spaces and weighted Bergman spaces with…
We introduce irregular constructible sheaves, which are $\mathbb{C}$-constructible with coefficients in a finite version of Novikov ring $\Lambda$ and special gradings. We show that the bounded derived category of cohomologically irregular…
The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral,…
Using the residue class rings we analyze the structure of sequences of musical intervals for the all-interval tone-semitone series and the quart modes as well. The relations we stated show the enharmonic return of the series to the initial…
The Springer correspondence makes a link between the characters of a Weyl group and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra. In this article, we consider a modular version of the theory, and show that…
A correspondence between quasicoherent sheaves on toric schemes and graded modules over some homogeneous coordinate ring is presented, and the behaviour of several finiteness properties under this correspondence is investigated.
The semi-group of weighted composition operators $(W_n)_{n\geq 1}$ where \[ W_nf(z)=(1+z+\ldots+z^{n-1})f(z^n) \] on the classical Hardy-Hilbert space $H^2$ of the open unit disk is related to the Riemann Hypothesis (RH) (see…
In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F.…
We survey nearby and vanishing cycles for both perverse sheaves and D-modules under analytic setting. Following ideas of A. Beilinson, M. Kashiwara and M. Saito, we explain in detail the proof of the comparison theorem between them in the…
In this paper we prove that the generating series of the Poincare polynomials of quasihomogeneous Hilbert schemes of points in the plane has a beautiful decomposition into an infinite product. We also compute the generating series of the…
Let $G$ be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic $p$. Let $I$ be a pro-$p$ Iwahori subgroup of $G$ and let $R$ be a commutative quasi-Frobenius ring. If…
We use the Gazeau-Klauder formalism to construct coherent states of non-Hermitian quantum systems. In particular we use this formalism to construct coherent state of a PT symmetric system. We also discuss construction of coherent states…
The study of cosmological correlators, and more generally Feynman integrals, is greatly aided by considering them as solutions to differential equations. Often, such systems of differential equations are reducible, which, broadly speaking,…
Using techniques of [BKV], we construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the regular-semisimple bounded locus of the loop group LG and prove that the derived $\tau$-coinvariants of affine…
Let $F$ be an arbitrary field and let $f:V\times V\to F$ be a non-degenerate symmetric or alternating bilinear form defined on an $F$-vector space of finite dimension $m\geq 2$. Let $L(f)$ be the subalgebra of $gl(V)$ formed by all…