Related papers: The Schur functor on tensor powers
We consider a family of Argyres-Douglas theories, which are 4D $\mathcal N=2$ strongly coupled superconformal field theories (SCFTs) but share many features with 4D $\mathcal N=4 $ super-Yang-Mills theories. In particular, the two central…
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction of symmetric functors provides an…
Derived functors (or Zuckerman functors) play a very important role in the study of unitary representations of real reductive groups. These functors are usually applied on highest weight modules in the so-called good range and the theory is…
Considering Schur positivity of differences of plethysms of homogeneous symmetric functions, we introduce a new relation on integer partitions. This relation is conjectured to be a partial order, with its restriction to one part partitions…
We obtain general identities for the product of two Schur functions in the case where one of the functions is indexed by a rectangular partition, and give their t-analogs using vertex operators. We study subspaces forming a filtration for…
The {\em Schubert derivation} is a distinguished Hasse-Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of Schubert calculus for all Grassmannians at once. The purpose of this paper is to extend the…
We consider families of quasisymmetric functions with the property that if a symmetric function $f$ is a positive sum of functions in one of these families, then f is necessarily a positive sum of Schur functions. Furthermore, in each of…
To any Schur polynomial $s_{\lambda}$ one can associated its derived polynomials $s_{\lambda}{(i)}$ $i=0,\ldots,|\lambda|$ by the rule $$s_{\lambda}(x_1+t,\ldots,x_n+t) = \sum_i s_{\lambda}^{(i)}(x_1,\ldots,x_n) t^i.$$ We conjecture that…
In this paper, the Schr{\"o}dinger equation in a magnetic field is utilized to study the effect of the magnetic field on $B$ mesons. The mass spetrum of $B$ mesons are numerically calculated for different magnetic field strengths by solving…
We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials,…
Given a module $M$ for the algebra $\mathcal{D}_{\mathtt{q}}(G)$ of quantum differential operators on $G$, and a positive integer $n$, we may equip the space $F_n^G(M)$ of invariant tensors in $V^{\otimes n}\otimes M$, with an action of the…
We show that a family of Dirichlet series generalizing the Fibonacci zeta function $\sum F(n)^{-s}$ has meromorphic continuation in terms of dihedral $\mathrm{GL}(2)$ Maass forms.
We prove some Schur positivity results for the chromatic symmetric function $X_G$ of a (hyper)graph $G$, using connections to the group algebra of the symmetric group. The first such connection works for (hyper)forests $F$: we describe the…
For two given symmetric sequence spaces $E$ and $F$ we study the $(E,F)$-multiplier space, that is the space all of matrices $M$ for which the Schur product $M\ast A$ maps $E$ into $F$ boundedly whenever $A$ does. We obtain several results…
In this article, we provide a comprehensive characterization of invariants of classical Lie superalgebras from the super-analog of the Schur-Weyl duality in a unified way. We establish $\mathfrak{g}$-invariants of the tensor algebra…
The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products…
Using symmetric function theory, we study the cycle structure and increasing subsequence structure of permutations after various shuffling methods, emphasizing the role of Cauchy type identities and the Robinson-Schensted-Knuth…
The immaculate functions, $\mathfrak{S}_{\alpha}$, were introduced as a Schur-like basis for $\operatorname{\mathsf{Nsym}}$. We investigate facts about their structure constants. These are analogues of Littlewood-Richardson coefficents. We…
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…
We establish a q-version of the Schur-Weyl duality, in which the role of the symmetric group is played by the Hecke algebra and the role of the enveloping algebra U(gl(N)) is played by the Reflection Equation algebra, associated with any…