Related papers: On the monoidality of Saito reflection functors
For arbitrary Coxeter systems, we prove that inverse Kazhdan-Lusztig polynomials satisfy a monotonicity property. This follows from the validity of Soergel's conjecture and the existence of injective morphisms between Rouquier complexes in…
We investigate a class of Kac-Moody algebras previously not considered. We refer to them as n-extended Lorentzian Kac-Moody algebras defined by their Dynkin diagrams through the connection of an $A_n$ Dynkin diagram to the node…
The Kac-Moody correction factor, first studied by Macdonald in the affine case, corrects the failure of an identity found by Macdonald in finite-dimensional root systems in 1972. Subsequntly this factor appeared in several formulas in the…
In a recent paper by K.-H. Lee and K. Lee, rigid reflections are defined for any Coxeter group via non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from an acyclic quiver, the rigid…
We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…
The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.
Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also…
We show that a suitable coset algebra, constructed in terms of an extension of the Zamolodchikov-Faddeev algebra, is homomorphic to the Reflection-Transmission algebra, as it appears in the study of integrable systems with impurity.
Davydov-Yetter cohomology $H_{\mathrm{DY}}^{\bullet}(F)$ is associated to a monoidal functor $F: \mathcal{C} \to \mathcal{D}$ between $\Bbbk$-linear monoidal categories where $\Bbbk$ is a field, and its second degree classifies the…
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many…
This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…
For every one-relator monoid $M = \langle A \mid u=v \rangle$ with $u, v \in A^*$ we construct a contractible $M$-CW complex and use it to build a projective resolution of the trivial module which is finitely generated in all dimensions.…
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…
Every monoidal functor G: C --> M has a canonical factorization through the category of bimodules over some monoid R in M such that the factor U: C -->_R M_R is strongly unital. Using this result and the characterization of the forgetful…
We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation theory of rational Cherednik algebras. In…
We prove that relative functors out of a cofibration category are essentially the same as relative functors which are only defined on the subcategory of cofibrations. As an application we give a new construction of the functor that assigns…
We provide an algorithm to calculate the invariant factors of the Shapovalov form on the standard $\Z$-lattice inside the basic representation of a Kac-Moody algebra of $ADE$ type, and give explicit formulae in some cases. The techniques…
Let $\Lambda$ be the category of based finite sets $\mathbf{n}$ and based injections. We study properties of monoids and modules in $\Lambda$-sequences under the Kelly monoidal structure. In particular, we show that the forgetful functor…
Mirror symmetry predicts an action by the fundamental group of a conjectural stringy K\"ahler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space is understood, but constructing the…
We study algebras defined by identities in symmetric monoidal categories. Our focus is on Lie algebras. Besides usual Lie algebras, there are examples appearing in the study of knot invariants and Rozansky-Witten invariants. Our main result…