Related papers: Plethysm and orbit harmonics
Let $h^\infty_v(\mathbf D)$ and $h^\infty_v(\mathbf B)$ be the spaces of harmonic functions in the unit disk and multi-dimensional unit ball which admit a two-sided radial majorant $v(r)$. We consider functions $v $ that fulfill a doubling…
We study rational homology groups of one-point compactifications of spaces of complex monic polynomials with multiple roots. These spaces are indexed by number partitions. A standard reformulation in terms of quotients of orbit arrangements…
We study harmonic Besov spaces $b^p_\alpha$ on the unit ball of $\mathbb{R}^n$, where $0<p<1$ and $\alpha\in\mathbb{R}$. We provide characterizations in terms of partial and radial derivatives and certain radial differential operators that…
We apply the theory of harmonic analysis on the fundamental domain of $SL(2,\mathbb{Z})$ to partition functions of two-dimensional conformal field theories. We decompose the partition function of $c$ free bosons on a Narain lattice into…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
Specializations of Schur functions are exploited to define and evaluate the Schur functions s_\lambda[\alpha X] and plethysms s_\lambda[\alpha s_\nu(X))] for any \alpha - integer, real or complex. Plethysms are then used to define pairs of…
Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…
The Fon-Der-Flaass action partitions the order ideals of a poset into disjoint orbits. For a product of two chains, Propp and Roby observed --- across orbits --- the mean cardinality of the order ideals within an orbit to be invariant. That…
We give new classes of examples of orbits of the diagonal group in the space of unit volume lattices in R^d for d > 2 with nice (homogeneous) orbit closures, as well as examples of orbits with explicitly computable but irregular orbit…
In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay across walls of marginal stability in the space of Coulomb branch parameters, leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a…
We develop a graded version of the theory of cyclotomic q-Schur algebras, in the spirit of the work of Brundan-Kleshchev on Hecke algebras and of Ariki on q-Schur algebras. As an application, we identify the coefficients of the canonical…
It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…
The numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the…
Consider the moduli space, $\mathcal{M}_{d}$, of degree $d \geq 2$ polynomials over $\mathbb{C}$, with a marked critical point. Given $k \geq 0,\; p$ an odd prime, we show that the set $\Sigma_{k,1,p}$ of conjugacy classes of degree $p$…
P. Aluffi introduced in [1] a new graded algebra in order to conveniently express characteristic cycles in the theory of singular varieties. This algebra is attached to a surjective ring homomorphism $A\surjects B$ by taking a suitable…
Periodic orbits for the classical $\phi^4$ theory on the one dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, fixed and free boundary conditions. Through the process, we…
We consider the number of the $6$-regular partitions of $n$, $b_6(n)$, and give infinite families of congruences modulo $3$ (in arithmetic progression) for $b_6(n)$. We also consider the number of the partitions of $n$ into distinct parts…
We analyze quantum fluctuations around black hole solutions to the Jackiw-Teitelboim model. We use harmonic analysis on Euclidean AdS$_2$ to show that the logarithmic corrections to the partition function are determined entirely by…
Let $Hilb ^{p(t)}(P^n)$ be the Hilbert scheme of closed subschemes of $P^n$ with Hilbert polynomial $p(t) \in Q[t]$, and let $W:= \overline{W(\underline{b};\underline{a};r)}$ be the closure of the locus in $Hilb ^{p(t)}(P^n)$ of…
We compute the corrections to heterotic-string backgrounds with (2,0) world-sheet supersymmetry, up to two loops in sigma-model perturbation theory. We investigate the conditions for these backgrounds to preserve spacetime supersymmetry and…