Related papers: Betti Spectral Gluing
The paper deals with homogenisation problems for high-contrast symmetric convolution-type operators with integrable kernels in media with a periodic microstructure. We adapt the two-scale convergence method to nonlocal convolution-type…
In the wild nonabelian Hodge correspondence on curves, filtered Stokes G-local systems are regarded as the objects on the Betti side. In this paper, we demonstrate a construction of the moduli space of them, called the Betti moduli space,…
Cohomology of Specht modules for the symmetric group can be equated in low degrees with corresponding cohomology for the Borel subgroup B of the general linear group GL_d(k), but this has never been exploited to prove new symmetric group…
We analyze the spectral properties of a self-adjoint second-order differential operator $\hat{C}$, defined on the Hilbert space $L^2([-v_c, v_c])$ with Dirichlet boundary conditions. We derive the discrete spectrum $\{C_n\}$, prove the…
Given a unital action $\theta $ of an inverse monoid $S$ on an algebra $A$ over a filed $K$ we produce (co)homology spectral sequences which converge to the Hochschild (co)homology of the crossed product $A\rtimes_\theta S$ with values in a…
We extend the results by Froelich and Spronk and Turowska on the connection between operator synthesis and spectral synthesis for A(G) to second countable locally compact groups G. This gives us another proof that one-point subset of G is a…
We observe that on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of characteristic $p> h$ (where $h$ is the Coxeter number), with a given (generalized) central character are…
In this paper we study the category of discrete G-spectra for a profinite group G. We consider an embedding of module objects in spectra into a category of module objects in discrete G-spectra, and study the relationship between the…
Let $(E,\overline{\partial}_E,\theta)$ be a stable Higgs bundle of degree $0$ on a compact connected Riemann surface. Once we fix the flat metric $h_{\det(E)}$ on the determinant of $E$, we have the harmonic metrics $h_t$ $(t>0)$ for the…
For a split reductive group $G$ over a finite field, we show that the neutral block of its mixed Hecke category with a fixed monodromy under the torus action is monoidally equivalent to the mixed Hecke category of the corresponding…
In this paper we construct equivalences of monoidal categories relating three geometric or representation-theoretic categorical incarnations of the affine Hecke algebra of a connected reductive algebraic group $G$ over a field of positive…
We study the limiting behavior of the solutions $h_t$ of the Hitchin's equation associated with a family of stable SU(1,2) Higgs bundles $(L,F,t\beta,t\gamma)$ on a compact connected Riemann surface $X$ as $t\to\infty$ under the assumption…
We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of…
The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…
Given a finite subgroup G of SL(2,C) we define an additive 2-category H^G whose Grothendieck group is isomorphic to an integral form of the Heisenberg algebra. We construct an action of H^G on derived categories of coherent sheaves on…
We define the degenerate two boundary affine Hecke-Clifford algebra $\mathcal{H}_d$, and show it admits a well-defined $\mathfrak{q}(n)$-linear action on the tensor space $M\otimes N\otimes V^{\otimes d}$, where $V$ is the natural module…
We apply the ideas of derived algebraic geometry and topological field theory to the representation theory of reductive groups. Our focus is the Hecke category of Borel-equivariant D-modules on the flag variety of a complex reductive group…
In recent work Cortez and Petite defined odometer actions of discrete, finitely generated and residually finite groups G. In this paper we focus on the case where G is the discrete Heisenberg group. We prove a structure theorem for finite…
The notion of Hochschild cochains induces an assignment from $Aff$, affine DG schemes, to monoidal DG categories. We show that this assignment extends, under some appropriate finiteness conditions, to a functor $\mathbb H: Aff \to…
An important classification problem in Algebraic Geometry deals with pairs $(\E,\phi)$, consisting of a torsion free sheaf $\E$ and a non-trivial homomorphism $\phi\colon (\E^{\otimes a})^{\oplus b}\lra\det(\E)^{\otimes c}\otimes \L$ on a…