Related papers: Invariants of partitions and representative elemen…
We suggest a geometrical approach to the semi-invariants of quivers based on Luna's slice theorem and the Luna-Richardson theorem. The locally semi-simple representations are defined in this spirit but turn out to be connected with stable…
The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra…
In this article we give an algorithm for determining the generators and relations for the rings of semi-invariant functions on irreducible components of representation spaces for gentle string algebras. These rings of semi-invariants turn…
We study properties of convex hulls of (co)adjoint orbits of compact groups, with applications to invariant theory and tensor product decompositions. The notion of partial convex hulls is introduced and applied to define two numerical…
Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a central role in geometric representation theory. A new structure on this variety has arisen in several representation theoretic constructions, such as…
For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds…
We present a novel approach to generate a fingerprint for crystalline materials that balances efficiency for machine processing and human interpretability, allowing its application in both machine learning inference and understanding of…
A method based on the symbolic methods of the classical invariant theory is developed for a representation of elements of kernel of Weitzenb\"ok derivations.
For an irreducible complex reflection group $W$ of rank $n$ containing $N$ reflections, we put $g=2N/n$ and construct a $(g+1)^n$-dimensional irreducible representation of the Cherednik algebra which is (as a vector space) a quotient of the…
Properties of invariant, anti-invariant and slant isometrically immersed submanifolds of metallic Riemannian manifolds are given with a special view towards the induced $\Sigma$-structure. Examples of such metallic manifolds are also given.
Let $\mathbf{G}(\mathsf{k})$ be a semisimple $p$-adic group, inner to split. In this article, we compute the algebraic and canonical unramified wavefront sets of the irreducible supercuspidal representations of $\mathbf{G}(\mathsf{k})$ in…
This is my PhD thesis supervised by Professor Jerzy Weyman. A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows…
The Robinson-Schensted correspondence can be viewed as a map from permutations to partitions. In this work, we study the number of inversions of permutations corresponding to a fixed partition $\lambda$ under this map. Hohlweg characterized…
Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes…
For $\mathfrak{g}$ a simple Lie algebra and $G$ its adjoint group, the Chevalley map and work of Coxeter gives a concrete description of the algebra of $G$-invariant polynomials on $\mathfrak{g}$ in terms of traces over various…
A surface in a three-dimensional metric Lie group $G$ is said invariant if it is invariant with respect to a one-dimensional subgroup $\Gamma$ of the isometry group of $G$. Is this work we focus on unimodular metric Lie groups $G$ that can…
Two classical rings of invariants are shown to be Frobenius split: for the special linear group acting on the direct sum of several copies of the defining representation and several copies of the dual of the defining representation; and for…
The classical Robinson--Schensted--Knuth correspondence is a bijection from nonnegative integer matrices to pairs of semi-standard Young tableaux. Based on the work of, among others, Burge, Hillman, Grassl, Knuth and Gansner, it is known…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
We introduce a multivariable Casson-Lin type invariant for links in $S^3$. This invariant is defined as a signed count of irreducible $\operatorname{SU}(2)$ representations of the link group with fixed meridional traces. For 2-component…