Related papers: Parking Spaces

This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…

Let $R$ be a commutative Noetherian ring. We introduce the notion of localization functors $\lambda^W$ with cosupports in arbitrary subsets $W$ of $\text{Spec}\, R$; it is a common generalization of localizations with respect to…

Let $(W,S)$ be a Coxeter system and $\Gamma$ be a group of automorphisms of $W$ such that $\gamma(S)=S$ for all $\gamma \in \Gamma$. Then it is known that the group of fixed points $W^\Gamma$ is again a Coxeter group with a canonically…

We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…

This is the first in a series of papers, where we introduce and study topological spaces that realize the algebras of quasi-invariants of finite reflection groups. Our result can be viewed as a generalization of a well-known theorem of A.…

We define a new lattice structure on the elements of a finite Coxeter group W. This lattice, called the shard intersection order, is weaker than the weak order and has the noncrossing partition lattice NC(W) as a sublattice. The new…

The paper is about methods of discrete Fourier analysis in the context of Weyl group symmetry. Three families of class functions are defined on the maximal torus of each compact simply connected semisimple Lie group $G$. Such functions can…

Factoring out the spin $1$ subalgebra of a $ W $ algebra leads to a new $ W $ structure which can be seen either as a rational finitely generated $ W $ algebra or as a polynomial non-linear $ W_\infty$ realization.

In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of $\hat w$-operators. In this letter, we demonstrate that…

In this note, we study the polynomial representation of the quantum Olshanetsky-Perelomov system for a finite reflection group $W$ of type $B_n$. We endow the polynomial ring ${\mathbb C} [x_1,\ldots\\\ldots, x_n]$ with a structure of…

The existence of apparently coincidental equalities (also called Wilf-equivalences) between the enumeration sequences, or generating functions, of various hereditary classes of combinatorial structures has attracted significant interest. We…

Let g be a complex semisimple Lie algebra, and f : g --> g/G the adjoint quotient map. Springer theory of Weyl group representations can be seen as the study of the singularities of f. We give a generalization of Springer theory to visible,…

For an irreducible complex reflection group $W$ of rank $n$ containing $N$ reflections, we put $g=2N/n$ and construct a $(g+1)^n$-dimensional irreducible representation of the Cherednik algebra which is (as a vector space) a quotient of the…

We introduce a generalization of parking functions called $t$-metered $(m,n)$-parking functions, in which one of $m$ cars parks among $n$ spots per hour then leaves after $t$ hours. We characterize and enumerate these sequences for $t=1$,…

Consider $n$ cars $C_1, C_2, \ldots, C_n$ that want to park in a parking lot with parking spaces $1,2,\ldots,n$ that appear in order. Each car $C_i$ has a parking preference $\alpha_i \in \{1,2,\ldots,n\}$. The cars appear in order, if…

On a compact connected group $G$, consider the infinitesimal generator $-L$ of a central symmetric Gaussian convolution semigroup $(\mu_t)_{t>0}$. We establish several regularity results of the solution to the Poisson equation $LU=F$, both…

We construct a Weil-Petersson geodesic completion of Teichmuller space through the formalism of Coxeter complex with the Teichmuller space as its non-linear non-homogeneous fundamental domain. We show that the metric and geodesic…

We extend the notion of parking functions to parking sequences, which include cars of different sizes, and prove a product formula for the number of such sequences.

We introduce the Hermitian-invariant group $\Gamma_f$ of a proper rational map $f$ between the unit ball in complex Euclidean space and a generalized ball in a space of typically higher dimension. We use properties of the groups to define…

We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R) / sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras.…