Related papers: Deformed Harish-Chandra homomorphism for the cycli…
In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\i}ymaz O. A certain generalized Pochhammer symbol and its…
In this paper one considers three homotopy functors on the category of manifolds, $hH^\ast, cH^\ast, sH^\ast,$ and parallel them with other three homotopy functors on the category of connected commutative differential graded algebras,…
We discuss the geometry of the c-map from projective special K\"ahler to quaternionic K\"ahler manifolds using the twist construction to provide a global approach to Hitchin's description. As found by Alexandrov et al. and Alekseevsky et…
We give a brief review of holomorphic motions and its relation with quasiconformal mapping theory. Furthermore, we apply the holomorphic motions to give new proofs of famous Konig's Theorem and Bottcher's Theorem in classical complex…
For a smooth finite cyclic covering over a projective space of dimension greater than one, we show that the group of automorphisms acts faithfully on the cohomology except for a few cases. In characteristic zero, we study the equivariant…
We give the exact contributions of Harish-Chandra transform, $(\mathcal{H}f)(\lambda),$ of Schwartz functions $f$ to the harmonic analysis of spherical convolutions and the corresponding $L^{p}-$ Schwartz algebras on a connected semisimple…
This paper is our first step in establishing a de Rham model for equivariant twisted $K$-theory using machinery from noncommutative geometry. Let $G$ be a compact Lie group, $M$ a compact manifold on which $G$ acts smoothly. For any $\alpha…
Using Bloch-Ogus theorem and Chern character from K-theory to cyclic homology, we answer a question of Green and Griffiths on extending Bloch formula. Moreover, we construct a map from local Hilbert functor to local cohomology. With…
Recently, two of the authors of this paper constructed cyclic cocycles on Harish-Chandra's Schwartz algebra of linear reductive Lie groups that detect all information in the $K$-theory of the corresponding group $C^*$-algebra. The main…
This paper contains a non-trivial generalization of the Harish-Chandra transforms on a connected semisimple Lie group $G,$ with finite center, into what we term spherical convolutions. Among other results we show that its integral over the…
We give a new and simple proof of the Hankel inversion formula for the classical Hankel transform which holds for a complex order with real part greater than -1. Using the proof of this formula we obtain the full description of the Kirillov…
We describe the Gerstenhaber bracket structure on Hochschild cohomology of Koszul quiver algebras in terms of homotopy lifting maps. There is a projective bimodule resolution of Koszul quiver algebras that admits a comultiplicative…
We prove a variant of the Chance-McDuff conjecture for pseudo-rotations: under certain additional conditions, a closed symplectic manifold which admits a Hamiltonian pseudo-rotation must have deformed quantum product and, in particular,…
We show that for any finite connected reductive group, a Jordan decomposition can always be chosen such that it commutes with Harish-Chandra induction. En route, we show that the endomorphism algebra of the Harish-Chandra induction of a…
Based on a construction by Kashiwara and Rouquier, we present an analogue of the Beilinson- Bernstein localization theorem for hypertoric varieties. In this case, sheaves of differential operators are replaced by sheaves of W-algebras. As a…
We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss-Manin connection on periodic cyclic…
We analyze the centralizer of the Macdonald difference operator in an appropriate algebra of Weyl group invariant difference operators. We show that it coincides with Cherednik's commuting algebra of difference operators via an analog of…
We generalise the classical Bass-Heller-Swan decomposition for the K-theory of (twisted) Laurent algebras to a splitting for general localising invariants of certain categories of twisted automorphisms. As an application, we obtain…
In this paper, we consider Hessian equations with its structure as a combination of elementary symmetric functions on closed K\"ahler manifolds. We provide a sufficient and necessary condition for the solvability of these equations, which…
We prove the K\"unneth formula for the irregular Hodge filtrations on the exponentially twisted de Rham and the Higgs cohomologies of smooth quasi-projective complex varieties. The method involves a careful comparison of the underlying…