Related papers: Three Examples of Quasisymmetric Compatible $\math…

We consider symmetric polynomials, p, in the noncommutative free variables (x_1, x_2, ..., x_g). We define the noncommutative complex hessian of p and we call a noncommutative symmetric polynomial noncommutative plurisubharmonic if it has a…

We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups $\operatorname{GL}_n$, the two-parameter…

Let R be a ring of polynomials in a finite number of variables over a perfect field k of characteristic p>0 and let F:R\to R be the Frobenius map of R, i.e. F(r)=r^p. We explicitly describe an R-module isomorphism Hom_R(F_*(M),N)\cong…

Let $n$ be a nonnegative integer. For each composition $\alpha$ of $n$, Berg $\textit{et al.}$ introduced a cyclic indecomposable $H_n(0)$-module $\mathcal{V}_\alpha$ with a dual immaculate quasisymmetric function as the image of the…

We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound…

For a closed connected manifold N, we construct a family of functions on the Hamiltonian group G of the cotangent bundle T^*N, and a family of functions on the space of smooth functions with compact support on T^*N. These satisfy properties…

Recently, an intriguing correspondence was conjectured in arXiv:2409.11551 between Schur half-indices of pure 4d $SU(2)$ $\mathcal{N}=2$ supersymmetric Yang-Mills (SYM) theory with line operator insertions and partition functions of the…

We use crystals of tableaux and descent compositions to understand the decomposition of Schur functions $s_\lambda$ into Gessel's fundamental quasisymmetric functions $F_\alpha$. The connected crystal of tableaux $B(\lambda)$, associated to…

In this paper, we use Schur elements to derive semisimplicity criteria for (super)symmetric superalgebras. We obtain a closed formula for the Schur elements of cyclotomic Hecke-Clifford superalgebras $\mathcal{H}^{f}_{\mathbb{K}}$. As…

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form $<,>$ on…

An important open problem in geometric complex analysis is to find algorithms for explicit determination of basic functionals intrinsically connected with conformal and quasiconformal maps, such as their Teichmuller and Grunsky norms,…

We introduce generalized Frobenius-Schur indicators for pivotal categories. In a spherical fusion category C, an equivariant indicator of an object in C is defined as a functional on the Grothendieck algebra of the quantum double Z(C) via…

Directional notions in topology and analysis naturally lead to nonsymmetric structures such as quasi-metrics, quasi-uniformities, and modular spaces. In these settings, classical notions of connectedness and completion based on symmetric…

We formulate N-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of N-fold supersymmetry, namely, almost isospectrality and weak…

We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective)…

Motivated by questions originating from the study of a class of shallow student-teacher neural networks, methods are developed for the analysis of spurious minima in classes of gradient equivariant dynamics related to neural nets. In the…

A classical result of Artin states that the ideal generated by symmetric polynomials in $n$ variables is of codimension $n!$. The author, F. Bergeron and N. Bergeron have recently obtained a surprising analogous in the case of…

It is known that there is no finitely presented group for which the Dehn function lies asymptotically strictly between linear and quadratic functions. This work presents an example of a semigroup that has Dehn function equivalent to $n \log…

We define, for each subset $S$ of the set $\mathcal{P}$ of primes, an $S_n$-module $Lie_n^S$ with interesting properties. $Lie_n^\emptyset$ is the well-known representation $Lie_n$ of $S_n$ afforded by the free Lie algebra, while…

The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothendieck ring of the category of finitely generated…