We study linear free divisors, that is, free divisors arising as discriminants in prehomogeneous vector spaces, and in particular in quiver representation spaces. We give a characterization of the prehomogeneous vector spaces containing such linear free divisors. For reductive linear free divisors, we prove that the numbers of geometric and representation theoretic irreducible components coinci...

Let EG be a stable principal G–bundle over a compact connected Kähler manifold, where G is a connected reductive linear algebraic group defined over C. Let H ⊂ G be a complex reductive subgroup which is not necessarily connected, and let EH ⊂ EG be a holomorphic reduction of structure group. We prove that EH is preserved by the Einstein–Hermitian connection on EG. Using this we show that if EH ...

Let G be a connected reductive algebraic group with Lie algebra g. The ground field k is algebraically closed and of characteristic zero. Fundamental results in invariant theory of the adjoint representation ofG are primarily associated with C. Chevalley and B. Kostant. Especially, one should distinguish the ”Chevalley restriction theorem” and seminal article of Kostant [5]. Later, Kostant and ...

Introduction. Let G be a reductive Lie group with maximal compact subgroup K and let Γ be a cocompact discrete subgroup of G. We consider the induced representation IndΓ (C), which is the canonical representation on the space L2(Γ\G). The duality theorem of Gelfand [6] states that there is a Frobenius reciprocity as follows: for any irreducible unitary representation π of G it holds HomG,cont(I...

Let $G$ be a reductive group over number field $F$, which is split at finite place $\mathfrak{p}$ of and let $\pi$ cuspidal automorphic representation $G$, cohomological with respect to the trivial coefficient system Steinberg $\mathfrak{p}$. We use cohomology $\mathfrak{p}$-arithmetic subgroups attach $\mathcal{L}$-invariants $\pi$. This generalizes construction Darmon (respectively Spie\ss), ...

Let G $G$ be an affine algebraic group defined over a field k $k$ of characteristic 0. We study the derived moduli space -local systems on pointed connected CW complex X $X$ trivialized at basepoint . This is represented by DG scheme R Loc ( , * ) $ \bm{\mathrm{R}}\mathrm{Loc}_G(X,\ast )$ : we call (co)homology structure sheaf representation homology in and denote it HR \mathrm{HR}_\ast (X,G)$ ...