Related papers: Z-linear Gale duality and poly weighted spaces (PW…

We discuss the theory of Poisson vertex algebras and their generalizations in relation to integrability of Hamiltonian PDE. In particular, we discuss the theory of affine classical W-algebras and apply it to construct a large class of…

We study the action of the Chevalley involution of a simple complex Lie group G on the set of its weight varieties (i.e. torus quotients of its flag manifolds). We find for torus quotients of Grassmannians (for GL(n)) that we obtain the…

The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…

We define a class of quantum linear Galois algebras which include the universal enveloping algebra Uq(gln), the quantum Heisenberg Lie algebra and other quantum orthogonal Gelfand-Zetlin algebras of type A, the subalgebras of G-invariants…

In this paper we give a combinatorial view on the adjunction theory of toric varieties. Inspired by classical adjunction theory of polarized algebraic varieties we define two convex-geometric notions: the Q-codegree and the nef value of a…

We study the algebra of Weyl modules in types $A$ and $C$ using the methods of arcs over toric degenerations and functional realization of dual space. We compute the generators and relations of this algebra and construct its basis.

In this paper we study dually flat spaces arising from Delzant polytopes equipped with a symplectic potential together with their corresponding toric K\"ahler manifolds as their torifications.We introduce a dually flat structure and the…

We analyze unoriented Wess-Zumino-Witten models from a geometrical point of view. We show that the geometric interpretation of simple current crosscap states is as centre orientifold planes localized on conjugacy classes of the group…

In this paper, we establish an innovative framework in logarithmic Hodge theory for toroidal varieties, introducing weighted toroidal structures and developing a systematic obstruction theory for Hodge classes. Building upon recent advances…

We discuss gauge theories for commutative but non-associative algebras related to the $ SO(2k+1)$ covariant finite dimensional fuzzy $2k$-sphere algebras. A consequence of non-associativity is that gauge fields and gauge parameters have to…

The aim of this article is to show that the transpose-dual pairs in the sense of Ebeling-Ploog of singularities $(Z_{1,0},\, Z_{1,0})$, $(U_{1,0},\, U_{1,0})$, $(Q_{17},\, Z_{2,0})$, $(W_{1,0},\, W_{1,0})$ that are concluded to be…

We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This…

We define and study a sheaf-theoretic cohomological Hall algebra for suitably geometric Abelian categories $\mathcal{A}$ of homological dimension at most two, and a sheaf-theoretic BPS algebra under the conditions that $\mathcal{A}$ is…

We develop the Dirac-Schwinger-Zwanziger (DSZ) quantization of classical abelian gauge theories with general duality structure on oriented Lorentzian four-manifolds $(M,g)$ of arbitrary topology, obtaining, as a result, the…

Let $X$ be a $\Q$-factorial complete toric variety over an algebraic closed field of characteristic $0$. There is a canonical injection of the Picard group ${\rm Pic}(X)$ in the group ${\rm Cl}(X)$ of classes of Weil divisors. These two…

We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over unital versions of binary quadratic operads. As an application, we study Poisson $n$-algebras given by polynomial functions on a…

Kazhdan-Lusztig-Stanley polynomials are a combinatorial generalization of Kazhdan-Lusztig polynomials of for Coxeter groups that include g-polynomials of polytopes and Kazhdan-Lusztig polynomials of matroids. In the cases of Weyl groups,…

For an affine, toric Q-Gorenstein variety Y (given by a lattice polytope Q) the vector space T^1 of infinitesimal deformations is related to the complexified vector spaces of rational Minkowski summands of faces of Q. Moreover, assuming Y…

In this paper we investigate gauged Wess-Zumino-Witten models for space-time groups as gravitational theories, following the trend of recent work by Anabalon, Willison and Zanelli. We discuss the field equations in any dimension and study…

Let $V$ be a free module of rank $n$ over a commutative unital ring $k$. We prove that tensor space $V^{\otimes r}$ satisfies Schur--Weyl duality, regarded as a bimodule for the action of the group algebra of the Weyl group of…