Related papers: Ind--varieties of generalized flags as homogeneous…

In this paper a notion of {\it generalized 2-vector space} is introduced which includes Kapranov and Voevodsky 2-vector spaces. Various kinds of generalized 2-vector spaces are considered and examples are given. The existence of non free…

Let $G$ be a semisimple, simply connected, algebraic group over an algebraically closed field $k$ with Lie algebra $\frak g$. We study the spaces of parahoric subalgebras of a given type containing a fixed nil-elliptic element of $\frak…

Let $C \langle \boldsymbol{t} \rangle$ be the differential field generated by $l$ differential indeterminates $\boldsymbol{t}=(t_1, \dots, t_l)$ over an algebraically closed field $C$ of characteristic zero. In this article we present an…

We give a general framework of equivariant model category theory. Our groups G, called Hopf groups, are suitably defined group objects in any well-behaved symmetric monoidal category V. For any V, a discrete group G gives a Hopf group,…

In this short note, we prove a G-equivariant generalisation of McDuff-Segal's group-completion theorem for finite groups G. A new complication regarding genuine equivariant localisations arises and we resolve this by isolating a simple…

Let $\mathbb{F}$ be a field of characteristic different from $2$ and $3$, and let $V$ be a vector space of dimension $2$ over $\mathbb{F}$. The generic classification of homogeneous quadratic maps $f\colon V\to V$ under the action of the…

The Hecke algebras and quantum group of affine type A admit geometric realizations in terms of complete flags and partial flags over a local field, respectively. Subsequently, it is demonstrated that the quantum group associated to partial…

Let g be a semi-simple Lie algebra. In this paper we study the spaces of based quasi-maps from the projective line P^1 to the flag variety of g (it is well-known that their singularities are supposed to model the singularities of the so…

We prove a universal embedding theorem for flag manifolds: every flag manifold admits a holomorphic isometric embedding into an irreducible classical flag manifold. This result generalizes the classical celebrated embedding theorems of…

Let $X$ be a smooth projective connected curve of genus $g\ge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show…

We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out certain generic properties of finite-dimensional algebras, mostly over infinite fields.…

We study a new class of infinite-dimensional Lie algebras W_\infty(p,q) generalizing the standard W_\infty algebra, viewed as a tensor operator algebra of SU(1,1) in a group-theoretic framework. Here we interpret W_\infty(p,q) either as an…

This thesis consists of two parts which share only a slight overlap. The first part is concerned with the study of ideals in the ring $C^\infty(M,R)$ of smooth functions on a compact smooth manifold M or more generally submodules of a…

A finite hypergraph $H$ consists of a finite set of vertices $V(H)$ and a collection of subsets $E(H) \subseteq 2^{V(H)}$ which we consider as partition of unity relations between projection operators. These partition of unity relations…

Scalar relative invariants play an important role in the theory of group actions on a manifold as their zero sets are invariant hypersurfaces. Relative invariants are central in many applications, where they often are treated locally since…

We consider the ordinary category Span(C) of (isomorphism classes of) spans of morphisms in a category C with finite limits as needed, composed horizontally via pullback, and give a general criterion for a quotient of Span(C) to be an…

Let $G$ be one of the ind-groups $GL(\infty)$, $O(\infty)$, $Sp(\infty)$, and $P_1,\dots, P_l$ be an arbitrary set of $l$ splitting parabolic subgroups of $G$. We determine all such sets with the property that $G$ acts with finitely many…

We compute the algebra of differential invariants of unparametrized curves in the homogeneous G(2) flag varieties, namely in G(2)/P. This gives a solution to the equivalence problem for such curves. We consider the cases of integral and…

A geometric extension algebra is an extension algebra of a semi-simple perverse sheaf (allowing shifts), e.g. a push-forward of the constant sheaf under a projective map. Particular nice situations arise for collapsings of homogeneous…

We find upper and lower bounds of the multiplicities of irreducible admissible representations $\pi$ of a semisimple Lie group $G$ occurring in the induced representations $Ind_H^G\tau$ from irreducible representations $\tau$ of a closed…