共查询到20条相似文献,搜索用时 15 毫秒
1.
Let G = SpecA be an affine K-group scheme and à = {w ∈ A*: dim K A*·w < ∞, dim K w· A* < ∞}. Let 〈?,?〉: A* × Ã → K, 〈w, \(\tilde w\)〉:=tr(w~w), be the trace form. We prove that G is linearly reductive if and only if the trace form is non-degenerate on A*. 相似文献
2.
We prove a generalisation of a theorem of Nagata on ruled surface to the case of the fiber bundle E/P X, associated to a principal G-bundle E. Using this we prove boundedness for the isomorphism classes of semi-stable G-bundles in all characteristics. 相似文献
3.
G. Kemper 《Transformation Groups》2000,5(1):85-92
The theorem of Hochster and Roberts says that, for every moduleV of a linearly reductive groupG over a fieldK, the invariant ringK[V]
G is Cohen-Macaulay. We prove the following converse: ifG is a reductive group andK[V]
G is Cohen-Macaulay for every moduleV, thenG is linearly reductive. 相似文献
4.
Assume a fixed point v∈VG can be separated from zero by a homogeneous invariant f∈𝕜[V]G of degree prd, where p>0 is the characteristic of the ground field 𝕜 and p,d are coprime. We show that then v can also be separated from zero by an invariant of degree pr, which we obtain explicitly from f. It follows that the minimal degree of a homogeneous invariant separating v from zero is a p-power. 相似文献
5.
Robert M. Guralnick 《Proceedings of the American Mathematical Society》2007,135(3):689-693
We show that if is a reductive group, then th roots of conjugacy classes are a finite union of conjugacy classes, and that if is an algebraic overgroup of , then the intersection of with a conjugacy class of is a finite union of -conjugacy classes. These results follow from results on finiteness of unipotent classes in an almost simple algebraic group.
6.
A. Ramanathan 《Proceedings Mathematical Sciences》1996,106(4):421-449
We classify principal bundles on a compact Riemann surface. A moduli space for semistable principal bundles with a reductive
structure group is constructed using Mumford’s geometric invariant theory.
This is the second and concluding part of the thesis of late Professor A Ramanathan; the first part was published in the previous
issue. 相似文献
7.
Andrzej Kornacki 《Applications of Mathematics》1997,42(1):71-77
Necessary and sufficient conditions are derived for the inclusions
and
to be fulfilled where
are some classes of invariant linearly sufficient statistics (Oktaba, Kornacki, Wawrzosek (1988)) corresponding to the Gauss-Markov models
, respectively. 相似文献
8.
Tomohiro Uchiyama 《代数通讯》2013,41(12):4928-4944
Let G be a reductive group over a nonperfect field k. We study rationality problems for Serre’s notion of complete reducibility of subgroups of G. In our previous work, we constructed examples of subgroups H of G that are G-completely reducible but not G-completely reducible over k (and vice versa). In this article, we give a theoretical underpinning of those constructions. Then using Geometric Invariant Theory, we obtain a new result on the structure of G(k)-(and G-) orbits in an arbitrary affine G-variety. We discuss several related problems to complement the main results. 相似文献
9.
M. S. Raghunathan 《Proceedings Mathematical Sciences》1989,99(2):127-146
It is shown in this paper that ifG is the group ofk-points of a semisimple algebraic groupG over a local fieldk of positive characteristic such that all itsk-simple factors are ofk-rank 1 and Γ ⊂G is a non-cocompact irreducible lattice then Γ admits a fundamental domain which is a union of translates of Siegel domains.
As a consequence we deduce that ifG has more than one simple factor, then Γ is finitely generated and by a theorem due to Venkataramana, it is arithmetic. 相似文献
10.
Andrei Minchenko 《代数通讯》2013,41(12):5094-5100
For a partial differential field K, we show that the triviality of the first differential Galois cohomology of every linear differential algebraic group over K is equivalent to K being algebraically, Picard–Vessiot, and linearly differentially closed. This cohomological triviality condition is also known to be equivalent to the uniqueness up to an isomorphism of a Picard–Vessiot extension of a linear differential equation with parameters. 相似文献
11.
Stephan Neupert 《Mathematische Nachrichten》2014,287(4):405-431
For connected reductive groups G over a finite extension F of and L the maximal unramified extension of F we study the sets of elements with given Hodge points . We explain the relationship to stratifications of some moduli scheme of abelian varieties defined by Goren and Oort respectively Andreatta and Goren. We show that for sufficiently large N the Newton point is constant on the sets and compute such N for certain classes of groups. 相似文献
12.
Yiu Tung Poon 《Linear and Multilinear Algebra》2013,61(1-3):221-223
Let A 1,…,Am be nxn hermitian matrices. Definine W(A 1,…,Am )={(xA1x ?,…xAmx ?):x?C n ,xx ?=1}. We will show that every point in the convex hull of W(A 1,…,Am ) can be represented as a convex combination of not more than k(m,n) points in W(A 1,…,Am ) where k(m,n)=min{n,[√m]+δ n 2 m+1}. 相似文献
13.
Pallav Goyal 《代数通讯》2018,46(10):4511-4529
14.
We describe two methods for computing with the elements of untwisted groups of Lie type: using the Steinberg presentation and using highest weight representations. We give algorithms for element arithmetic within the Steinberg presentation. Conversion between this presentation and linear representations is achieved using a new generalisation of row and column reduction.
15.
16.
In this paper we give an asymptotic formula for a matrix integral which plays a crucial role in the approach of Diaconis et al. to random matrix eigenvalues. The choice of parameter for the asymptotic analysis is motivated by an invariant-theoretic interpretation of this type of integral. For arbitrary regular irreducible representations of arbitrary connected semisimple compact Lie groups, we obtain an asymptotic formula for the trace of permutation operators on the space of tensor invariants, thus extending a result of Biane on the dimension of these spaces.
17.
Colin J. Bushnell Philip C. Kutzko 《Proceedings of the American Mathematical Society》2001,129(2):601-607
In this paper, is a non-Archimedean local field and is the group of -points of a connected reductive algebraic group defined over . Also, is an irreducible representation of a compact open subgroup of , the pair being a type in . The pair is assumed to be a cover of a type in a Levi subgroup of . We give conditions, generalizing those of earlier work, under which the Hecke algebra is the tensor product of a canonical image of and a sub-algebra , for a compact open subgroup of containing .
18.
It is well-known, that the ring of polynomial invariants of the alternating group has no finite SAGBI basis with respect to the lexicographical order for any number of variables . This note proves the existence of a nonsingular matrix such that the ring of polynomial invariants , where denotes the conjugate of with respect to , has a finite SAGBI basis for any . 相似文献
19.
We review the proposal of a constructive axiomatic approach to the determination of the orbit spaces of all the real compact linear groups, obtained through the computation of a metric matrix
, which is defined only in terms of the scalar products between the gradients p1(x),...,pq(x) of the elements of a minimal integrity basis (MIB) for the ring [n]G of G-invariant polynomials. The domain of semi-positivity of
is known to realize the orbit space n/G of G as a semi-algebraic variety in the space q spanned by the variables p1,...,pq.
The matrices
can be obtained from the solutions of a universal differential equation (master equation), which satisfy convenient initial conditions. The master equation and the initial conditions involve as free parameters only the degrees da of the pa(x)s. This approach tries to bypass the actual impossibility of explicitly determining a set of basic polynomial invariants for each group.
Our results may be relevant in physical contexts where the study of covariant or invariant functions is important, like in the determination of patterns of spontaneous symmetry breaking in quantum field theory, in the analysis of phase spaces and structural phase transitions (Landaus theory), in covariant bifurcation theory, in crystal field theory and so on.
Mathematics Subject Classifications (2000) 14L24, 13A50, 14L30.This paper is partially supported by INFN and MURST 40% and 60%. 相似文献
20.
Antoine Touzé 《Advances in Mathematics》2010,225(1):33-68
We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study of classical algebraic groups, such as a cohomological stabilization property, the injectivity of external cup products, and the existence of Hopf algebra structures on the (stable) cohomology of a classical algebraic group with coefficients in a Hopf algebra. Our result also opens the way to new explicit cohomology computations. We give an example inspired by recent computations of Djament and Vespa. 相似文献