Related papers: Weyl Groups Associated with Affine Reflection Syst…
We obtain Drinfeld second realization of the quantum affine superalgebras associated with the affine Lie superalgebra $D^{(1)}(2,1;x)$. Our results are analogous to those obtained by Beck for the quantum affine algebras. Beck's analysis…
We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system $\tilde{A}_n$, generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is…
We introduce the notion of 321-avoiding permutations in the affine Weyl group $W$ of type $A_{n-1}$ by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey,…
Given a grading $\Gamma: A=\oplus_{g\in G}A_g$ on a nonassociative algebra $A$ by an abelian group $G$, we have two subgroups of the group of automorphisms of $A$: the automorphisms that stabilize each homogeneous component $A_g$ (as a…
We propose quantum Painlev\'e systems of type $A_l^{(1)}$. These systems, for $l=1$ and $l\ge 2$, should be regarded as quantizations of the second Painlev\'e equation and the differential systems with the affine Weyl group symmetries of…
The theory of generalized Weyl algebras is used to study the $2\times 2$ reflection equation algebra $\mathcal{A}=\mathcal{A}_q(\operatorname{M}_2)$ in the case that $q$ is not a root of unity, where the $R$-matrix used to define…
We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules…
In this work, we theoretically investigate the superluminal and subluminal reflected group delay from an air-Weyl semimetal film-Weyl semimetal substrate layered structure by using 4*4 magneto-optical matrix. We show a tunable transition…
We present a new class of extended affine Weyl groups $\widetilde{W}^{(k,k+1)}(A_l)$ for $1\leq k <l$ and obtain an analogue of Chevalley-type theorem for their invariants. We further show the existence of Frobenius manifold structures on…
Motivated by the study of duality cascades in supersymmetric quiver gauge theories beyond affine models, we develop in this paper the analysis of a class of simply laced hyperbolic Lie algebras. These are specific generalizations of affine…
We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…
We extend properties of the weak order on finite Coxeter groups to Weyl groupoids admitting a finite root system. In particular, we determine the topological structure of intervals with respect to weak order, and show that the set of…
Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners, and describe the…
We find a two-parameter family of coupled Painlev\'e systems in dimension four with affine Weyl group symmetry of type $A_4^{(2)}$. For a degenerate system of $A_4^{(2)}$ system, we also find a one-parameter family of coupled Painlev\'e…
We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…
Let W be a finite group generated by unitary reflections and A be the set of reflecting hyperplanes. We will give a characterization of the logarithmic differential forms with poles along A in terms of anti-invariant differential forms. If…
We show that for general-type self-adjoint and skew-self-adjoint Dirac systems on the semi-axis Weyl functions are unique analytic extensions of the reflection coefficients. New results on the extension of the Weyl functions to the real…
Given a grading on a nonassociative algebra by an abelian group, we have two subgroups of automorphisms attached to it: the automorphisms that stabilize each homogeneous component (as a subspace) and the automorphisms that permute the…
Let A = (A,V) be a complex hyperplane arrangement and let L(A) denote its intersection lattice. The arrangement A is called supersolvable, provided its lattice L(A) is supersolvable. For X in L(A), it is known that the restriction A^X is…
Cherednik attached to an affine Hecke algebra module a compatible system of difference equations, called quantum affine Knizhnik-Zamolodchikov (KZ) equations. In case of a principal series module we construct a basis of power series…