Related papers: Invariant valuations on quaternionic vector spaces

To any Hamiltonian action of a reductive algebraic group $G$ on a smooth irreducible symplectic variety $X$ we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. For cotangent bundles our…

We describe a collection of computer scripts written in PARI/GP to compute, for reflection groups determined by finite-volume polyhedra in $\mathbb{H}^3$, the commensurability invariants known as the invariant trace field and invariant…

We develop explicit formulae for the eigenvalues of various invariants for highest weight irreducible representations of the quantum supergroup $U_q[gl(m|n)]$. The techniques employed make use of modified characteristic identity methods and…

We study the finite dimensional spaces $V$ which are invariant under the action of the finite differences operator $\Delta_h^m$. Concretely, we prove that if $V$ is such an space, there exists a finite dimensional translation invariant…

In our previous papers we repeatedly emphasized the special role in Quaternionic Analysis of the conformal group SU(2,2) and other real forms of its complexification SL(4,C). In particular, the natural product map of the left and right…

We propose an algorithm for computing bases and dimensions of spaces of invariants of Weil representations of $\mathrm{SL}_2(\mathbb{Z})$ associated to finite quadratic modules. We prove that these spaces are defined over $\mathbb{Z}$, and…

We provide a new proof of Alesker's Irreducibility Theorem. We first introduce a new localization technique for polynomial valuations on convex bodies, which we use to independently prove that smooth and translation invariant valuations are…

We provide a classification of type AII topological quantum systems in dimension d=1,2,3,4. Our analysis is based on the construction of a topological invariant, the FKMM-invariant, which completely classifies "Quaternionic" vector bundles…

We consider the most general SU(3) singlet space of gauged N=8 supergravity in four-dimensions. The SU(3)-invariant six scalar fields in the theory can be viewed in terms of six real four-forms. By exponentiating these four-forms, we…

We consider the Whitney problem for valuations: does a smooth $j$-homogeneous translation-invariant valuation on $\mathbb R^n$ exist that has given restrictions to a fixed family $S$ of linear subspaces? A necessary condition is…

For a symmetric space (G,H), one is interested in understanding the vector space of H-invariant linear forms on a representation \pi of G. In particular an important question is whether or not the dimension of this space is bounded by one.…

We analyse the strong connections between spaces of vector-valued Lipschitz functions and spaces of linear continuous operators. We apply these links to study duality, Schur properties and norm attainment in the former class of spaces as…

We consider each of the three classes of representations of cyclic groups that arise in the study of rational sphere maps. We study the possible number of terms for invariant polynomials with non-negative coefficients that are constant on…

In this paper we study the static Einstein-Maxwell space when it is conformal to an $n$-dimensional pseudo-Euclidean space, which is invariant under the action of an $(n-1)$-dimensional translation group. We also provide a complete…

In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

All measurable and $\operatorname{SL}(n)$-covariant vector valued valuations on convex polytopes containing the origin in their interiors are completely classified. The moment vector is shown to be essentially the only such valuation.

We reconsider an old problem, namely the dimension of the $G$-invariant subspace in $V^{\otimes p} \otimes V^{*\otimes q}$, where $G$ is one of the classical groups ${\rm GL}(V)$, ${\rm SL}(V)$, ${\rm O}(V)$, ${\rm SO}(V)$, or ${\rm…

Bi-Hamiltonian hierarchies of soliton equations are derived from geometric non-stretching (inelastic) curve flows in the Hermitian symmetric spaces $SU(n+1)/U(n)$ and $SO(2n)/U(n)$. The derivation uses Hasimoto variables defined by a moving…

An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, T-unitarizable representations of the full modular group, of dimension…