A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties.
A Hilbert-Mumford criterion for SL₂-actions
Let the special linear group G : = SL₂ act regularly on a ℚ-factorial variety X. Consider a maximal torus T ⊂ G and its normalizer N ⊂ G. We prove: If U ⊂ X is a maximal open N-invariant subset admitting a good quotient U → U ⃫N with a divisorial quotient space, then the intersection W(U) of all translates g · U is open in X and admits a good quotient W(U) → W(U) ⃫G with a divisorial quotient space. Conversely, we show that every maximal open G-invariant subset W ⊂ X admitting a good quotient W...
A Mackey Imprimitivity Theory for Algebraic Groups.
A minimal Set of Generators for the Ring of multisymmetric Functions
The purpose of this article is to give, for any (commutative) ring , an explicit minimal set of generators for the ring of multisymmetric functions as an -algebra. In characteristic zero, i.e. when is a -algebra, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving the degree bound previously...
A Modular Construction of Unramified p-Extension of Q (...).
A motivic isomorphism between two projective homogeneous varieties under the action of a group of type . (Un isomorphisme motivique entre deux variétés homogènes projectives sous l'action d'un groupe de type .)
A new compactification of the moduli space of curves
A nonlinearizable action of on
The main purpose of this article is to give an explicit algebraic action of the group of permutations of 3 elements on affine four-dimensional complex space which is not conjugate to a linear action.
A note on certain Tannakian group schemes
In this note, we prove that the -fundamental group scheme is a birational invariant for smooth projective varieties. We prove that the -fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic curves, it turns out that the -fundamental group scheme and the Nori fundamental group scheme coincide. We also consider an extension of the Nori fundamental group scheme in positive characteristic using semi-essentially finite vector bundles, and prove that in...
A note on extensions of algebraic and formal gorups I.
A note on extensions of algebraic and formal groups II.
A note on formal groups and zeta functions.
A note on semisimple derivations of commutative algebras
A concept of a slice of a semisimple derivation is introduced. Moreover, it is shown that a semisimple derivation d of a finitely generated commutative algebra A over an algebraically closed field of characteristic 0 is nothing other than an algebraic action of a torus on Max(A), and, using this, that in some cases the derivation d is linearizable or admits a maximal invariant ideal.
A note on Steinberg modules and Frobenius splitting.
A note on the characters of the projective modules for the infinitesimal subgroups of a semisimple algebraic group.
A note on Z/p/-actions on K3 surfaces in odd characteristic p.
A recipe for finding open subsets of vector spaces with a good quotient
A remark on quiver varieties and Weyl groups
In this paper we define an action of the Weyl group on the quiver varieties with generic .
A remark on the orbit spaces under multiplicative group actions
A remarkable contraction of semisimple Lie algebras
Recently, E.Feigin introduced a very interesting contraction of a semisimple Lie algebra (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of . For instance, the algebras of invariants of both adjoint and coadjoint representations of are free, and also the enveloping algebra of is a free module over its centre.