Related papers: On analytic contravariant functors on free groups
In [arXiv:1509.02937], the notion of a module tensor category was introduced as a braided monoidal central functor $F\colon \mathcal{V}\longrightarrow \mathcal{T}$ from a braided monoidal category $\mathcal{V}$ to a monoidal category…
An Eggert-operad is a variant of Mac Lane's notion of a PROP, for which not only bijective maps, but all maps between standard finite sets, are part of the structure. We construct the free Eggert-operad and prove the universal property it…
We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that…
With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…
Modular operads relevant to string theory can be equipped with an additional structure, coming from the connected sum of surfaces. Motivated by this example, we introduce a notion of connected sum for general modular operads. We show that a…
Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a…
We show, in full generality, that Lusztig's $\mathbf{a}$-function describes the projective dimension of both indecomposable tilting modules and indecomposable injective modules in the regular block of the BGG category $\mathcal{O}$, proving…
We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…
We review Koszul duality in representation theory of category $ \cal O $, especially we give a new presentation of the Koszul duality functor. Combining this with work of Backelin, we show that the translation and Zuckerman functors are…
We prove a conjecture of Cautis and Sussan providing a categorification of the Boson-Fermion correspondence as formulated by Frenkel and Kac. We lift the Bernstein operators to infinite chain complexes in Khovanov's Heisenberg category H…
For every semi-simple Lie algebra one can construct the Drinfeld-Jimbo algebra U. This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U, Drinfeld used the KZ-equations to…
In this paper, for a compact Lie group action,we prove the anomaly formula and the functoriality of the equivariant Bismut-Cheeger eta forms with perturbation operators when the equivariant family index vanishes. In order to prove them, we…
Gauge-invariant operators can be specified by equivalence classes of permutations. We develop this idea concretely for the singlets of the flavour group $SO(N_f)$ in $U(N_c)$ gauge theory by using Gelfand pairs and Schur-Weyl duality. The…
Free and cofree equivariant spectra are important classes of equivariant spectra which represent equivariant cohomology theories on free equivariant spaces. Greenlees-Shipley and Pol and the author have given an algebraic model for rational…
The classification problem for simple $\mathfrak{sl}(2)$-modules leads in a natural way to the study of the category of finite rank torsion free $\mathfrak{sl}(2)$-modules and its subcategory of rational $\mathfrak{sl}(2)$-modules. We prove…
The homology of free Lie algebras with coefficients in tensor products of the adjoint representation working over Q contains important information on the homological properties of polynomial outer functors on free groups. The latter…
We apply the free product construction to various local algebras in algebraic quantum field theory. If we take the free product of infinitely many identical half-sided modular inclusions with ergodic canonical endomorphism, we obtain a…
We construct a comparison functor from the dual category of motivic homotopy category $\mathcal{SH}$ to the category of $\mathbb{A}^1$-invariant localizing motives $\operatorname{Mot}_{\operatorname{loc}}^{\mathbb{A}^1}$ in the sense of…
We report on two classes of autoequivalences of the category of Yetter-Drinfeld modules over a finite group, or, equivalently the Drinfeld center of the category of representations of a finite group. Both operations are related to the…
Involutive category theory provides a flexible framework to describe involutive structures on algebraic objects, such as anti-linear involutions on complex vector spaces. Motivated by the prominent role of involutions in quantum (field)…