Related papers: Totally nonnegative maximal tori and opposed Bruha…

This paper continues the investigation begun in arXiv:1906.05602 of extending the T1 theorem of David and Journ\'e, and optimal cancellation conditions, to more general weight pairs. The main additional tool developed here is a two weight…

Our first result is a noncommutative form of Jessen/Marcinkiewicz/Zygmund theorem for the maximal limit of multiparametric martingales or ergodic means. It implies bilateral almost uniform convergence with initial data in the expected…

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…

Let $G$ be a connected Lie group and $\hat G$ its unitary dual. We are interested in the part $\Lambda\subset\hat G$ which corresponds to the unitary highest weight representations of $G$. Then there are several topologies on $\Lambda$: The…

Let G be a reductive group over an algebraically closed field k of very good characteristic. The Lusztig-Vogan bijection is a bijection between the set of dominant weights for G and the set of irreducible G-equivariant vector bundles on…

If $K$ is a compact, connected, simply connected Lie group, its based loop group $\Omega K$ is endowed with a Hamiltonian $S^1 \times T$ action, where $T$ is a maximal torus of $K$. Atiyah and Pressley examined the image of $\Omega K$ under…

We consider the Lie algebra $\mathfrak{g}$ of a simple, simply connected algebraic group over a field of large positive characteristic. For each nilpotent orbit $\mathcal{O} \subseteq \mathfrak{g}$ we choose a representative $e\in…

Let $G=SL_n(\mathbb C)$ and $T$ be a maximal torus in $G$. We show that the quotient $T \backslash \backslash G/{P_{\alpha_1}\cap P_{\alpha_2}}$ is projectively normal with respect to the descent of a suitable line bundle, where…

Given a complex smooth quasi-projective variety $X$, a semisimple algebraic group $G$ defined over some non-archimedean local field $K$ and a Zariski dense representation $\varrho:\pi_1(X)\to G(K)$, we construct a $\varrho$-equivariant…

Let $G$ be a semisimple connected Lie group of non-compact type with finite center. Let $K<G$ be a maximal compact subgroup and $P<G$ be a minimal parabolic subgroup. For any pair $(F,x)$, where $F$ is a maximal flat in $G/K$ and $x \in…

In 2005 J.L. Waldspurger proved the following theorem: given a finite real reflection group $W$, the closed positive root cone is tiled by the images of the open weight cone under the action of the linear transformations $id-w$. Shortly…

We study a mapping $\tau_G$ of the cone ${\mathbf B}^+({\mathcal H})$ of bounded nonnegative self-adjoint operators in a complex Hilbert space ${\mathcal H}$ into itself. This mapping is defined as a strong limit of iterates of the mapping…

Let G be a compact connected Lie group with a maximal torus T\subsetG. In the context of Schubert calculus we obtain a canonical presentation for the integral cohomology ring H^{\ast}(G/T) of the complete flag manifold G/T. The result have…

The existence of maximal subrings in certain non-commutative rings, especially in rings which are integral over their centers, are investigated. We prove that if a ring $T$ is integral over its center, then either $T$ has a maximal subring…

The group of homeomorphisms of the closed interval that are absolutely continuous and have an absolutely continuous inverse was shown by Solecki to admit a natural Polish group topology $\tau_{ac}$. We show that, under mild conditions on a…

The goal of this diploma thesis is to give a detailed description of Kirillov's Orbit Method for the case of compact connected Lie groups. The theory of Kirillov aims at finding all irreducible unitary representations of a given Lie group…

We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge…

Toric $t$-designs, or equivalently $t$-designs on the diagonal subgroup of the unitary group, are sets of points on the torus over which sums reproduce integrals of degree $t$ monomials over the full torus. Motivated by the projective…

If $G$ is a compact Lie group, $T$ a maximal torus in $G$ (with Lie algebras $\mathfrak{g}$ and $\mathfrak{t}$ respectively) and $W$ the corresponding Weyl group, then the Berry-Robbins problem for $G$, as formulated by Sir Michael Atiyah…

We describe an algorithm which pattern embeds, in the sense of Woo-Yong, any Bruhat interval of a symmetric group into an interval whose extremes lie in the same right Kazhdan-Lusztig cell. This apparently harmless fact has applications in…