Related papers: Classification of invariant valuations on the quat…
We formulate a theory of invariants for the spin symmetric group in some suitable modules which involve the polynomial and exterior algebras. We solve the corresponding graded multiplicity problem in terms of specializations of the Schur…
We classify, up to orbit equivalence, the cohomogeneity one actions on the noncompact duals of the symmetric spaces G_2, SU_3 and the real oriented two-plane Grassmannians.
We consider two types of quotients of the integrable modules of $\hat{sl}_2$. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level-$k$. We describe monomial bases for the spaces of coinvariants,…
We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. With the help of…
We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere $S^{n-1}$. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded…
We prove the classification of the real vector subspaces of a quaternionic vector space by using a covariant functor which, to any pair formed of a quaternionic vector space and a real subspace, associates a coherent sheaf over the sphere.
The holonomy group $G$ of a pseudo-quaternionic-K\"ahlerian manifold of signature $(4r,4s)$ with non-zero scalar curvature is contained in $\Sp(1)\cdot\Sp(r,s)$ and it contains $\Sp(1)$. It is proved that either $G$ is irreducible, or $s=r$…
We describe a curious structure of the special orthogonal, special unitary, and symplectic groups that has not been observed, namely, they can be expressed as matrix products of their corresponding Grassmannians realized as involution…
We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $\mathrm{GL}_2(F)$, for its subgroups of matrices whose determinant has even (respectively trivial)…
We classify all self-dual Einstein four-manifolds invariant under a principal action of the three-dimensional Heisenberg group with non-degenerate orbits. The metrics are explicit and we find, in particular, that the Einstein constant can…
An important problem in quaternionic hyperbolic geometry is to classify ordered $m$-tuples of pairwise distinct points in the closure of quaternionic hyperbolic n-space, $\overline{{\bf H}_\bh^n}$, up to congruence in the holomorphic…
S. Alesker has shown that if $G$ is a compact subgroup of O(n) acting transitively on the unit sphere $S^{n-1}$ then the vector space $Val^G$ of continuous, translation-invariant, $G$-invariant convex valuations on $R^n$ has the structure…
We develope a new scheme for the construction of explicit complex-valued proper biharmonic functions on Riemannian Lie groups. We exploit this and manufacture many infinite series of uncountable families of new solutions on the special…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
For transcendental values of $q$ all bicovariant first order differential calculi on the coordinate Hopf algebras of the quantum groups $SL_q(n+1)$ and $Sp_q(2n)$ are classified. It is shown that the irreducible bicovariant first order…
We give a classification of the matrices in the unitary group U(1,1;H),where H is the division ring of the real quaternions. To this end, we consider the complex representation phi(P) for P in U(1,1;H). Next, we compute the characteristic…
A classification of upper semicontinuous, translation and dually epi-translation invariant valuations is established on the space of convex Lipschitz function on $\mathbb{R}$ with compact domain.
All SL($n$) contravariant vector valuations on polytopes in $\mathbb R^n$ are completely classified without any additional assumptions. The facet vector is defined. It turns out to be the unique such valuation for $n\geq3$. In dimension…
We classify totally geodesic submanifolds of the real Stiefel manifolds of orthogonal two-frames. We also classify polar actions on these Stiefel manifolds, specifically, we prove that the orbits of polar actions are lifts of polar actions…
The Lawrence-Krammer representation was used in $2000$ to show the linearity of the braid group. The problem had remained open for many years. The fact that the Lawrence-Krammer representation of the braid group is reducible for some…