arithmetic properties of algebraic groups adele groups

... fields (of positive characteristic) We not know how to argue the case of fields of positive characteristic directly One of the key technical points of this paper is the construction of certain algebraic ... naturally equivalent We give a proof of this proposition in appendix 14; the proof makes use of results of Section Let us write Aut(O) for the group of automorphisms of the formal disc Spec(O) The ... independent of the choice of the pair T ⊂ B − Proof The Bruhat decomposition of GK for the Borel subgroups BK , BK gives decompositions Gr = ∪ Sν = ∪ Tν and hence two filtrations of Gr by closures of Sν...

Ngày tải lên: 06/03/2014, 08:21

... distribution of the hot X-ray gas The high significance of the spatial offset of the centre of the total mass of the object from the centre of the baryonic mass peaks is a clear indicator of the presence ... telescope, and a brief overview of eROSITA Chapter discusses ICM cooling, AGN feedback and BCG properties of galaxy groups and results thereof Chapter presents the impact of ICM cooling, AGN feedback ... complete sample of 112 groups However, not all of them have high-quality X-ray data, and so only those groups with Chandra observations were selected, giving a sample of 27 galaxy groups One group,...

Ngày tải lên: 26/11/2015, 10:18

... list of the values when Bn is odd This question had also been the key to the main ideas behind the arithmetic properties of An , as described in [4] Figure depicts the 2-adic valuation of An ... by ν2 (n) the 2-adic valuation of n, defined as the highest power of that divides n Let s2 (n) equal to the sum of the binary digits of n the electronic journal of combinatorics 18(2) (2011), ... valuation of sequences counting Alternating Sign Matrices Journal of Integer Sequences, 12:1–21, 2009 [5] D Zeilberger Proof of the Alternating Sign Matrix conjecture Electronic Journal of Combinatorics,...

Ngày tải lên: 08/08/2014, 14:23

... eigenvalues of ϕ on Monsky-Washnitzer cohomology This result, modeled on Berthelot’s proof [Ber97] of the finiteness of rigid cohomology, ultimately relies on the computation of the eigenvalues of Frobenius ... uniqueness For the proof of Theorem 19 we need to study in more detail the Lie algebra g As the group G is pro -algebraic, it can be written as an inverse limit of algebraic groups lim Gα Its Lie ... — The arithmetic of fundamental groups, which in reversed order gives rise to the title of the present volume The workshop took place in Heidelberg, 8–12 February 2010, and the abstracts of all...

Ngày tải lên: 14/03/2014, 21:20

... Annals of Mathematics, 160 (2004), 683–704 Unique decomposition of tensor products of irreducible representations of simple algebraic groups By C S Rajan Abstract We show that a tensor product of ... emphasis on the arithmetical properties of the varieties defined by these characters Tensor products of GL(r)-modules We now come to the proof of Theorem for arbitrary r The proof will proceed ... on the rank of g, by the fact that any simple Lie algebra of rank l, has a simple subalgebra of rank l − We analyze the restriction of the numerator of the Weyl character formula of g to the...

Ngày tải lên: 14/03/2014, 22:20

... dealt with those of word groups In addition, the three kinds Those are norminal groups, verbal groups and adjectival definitions and classifications of metaphor have been focused on groups Semantically, ... objectives of the study, scope of the study, significance of the study, research questions and design of the study - Chapter 2, Literature Review, concentrates on two main issues including a review of ... phrases and offered the definition of phrase and its BACKGROUND characteristics, especially, they showed and analyzed the types of Besides the review of previous studies, the author of the phrase...

Ngày tải lên: 26/11/2013, 13:16

... were the word groups denoting HIFs which included nominal groups, verbal groups, adjectival groups and prepositional groups in English, and nominal groups, verbal groups, adjectival groups in Vietnamese ... were the word groups denoting HIFs which included nominal groups, verbal groups, adjectival groups and prepositional groups in English, and nominal groups, verbal groups, adjectival groups in Vietnamese ... references of its Table 4.1 A Summary of Syntactic Features of Word Groups author(s), the name of publishers, the time and place of publication as Denoting Word Groups Denoting HIFs in PDs well as...

Ngày tải lên: 26/11/2013, 13:17

... destruction of the basic modes of subsistence of Human Ecology Review, Vol 8, No 1, 2001 Adeola the resource-dependent communities of indigenous minority groups The unique cases of selected minority groups ... exploitation, and the consequent degradation of the means of subsistence of indigenous people The roles of the state and MNCs in suppressing the rights of communal groups to a safe and sound environment ... percent of the officially acknowledged volume of exported hazardous waste is channeled to less developed nations The number of countries involved in export and import schemes, volume of trade, and properties...

Ngày tải lên: 15/03/2014, 23:20

... version of a theorem of Nakajima and realization of p-compact groups Nontoral elementary abelian p-subgroups of simple center-free Lie groups 8.1 Recollection of some results on linear algebraic groups ... connected Lie groups are uniquely determined as p-compact groups by their Weyl groups, seen as Zp -reflection groups In fact our method of proof gives an essentially self-contained proof of the entire ... builds upon Skeleton of the proof of the main Theorems 1.1 and 1.4 The purpose of this section is to give the skeleton of the proof of the main Theorems 1.1 and 1.4, but in the proofs referring forward...

Ngày tải lên: 22/03/2014, 20:21

Ngày tải lên: 27/03/2014, 11:48

... neighborhood W of Gx in G there is an open neighborhood ~ ~ W of Gx such that Gx :W W Proof: The proof relies on the compactness of Gx Choose for all (a b) Gx Gx neighborhoods Aa b of a and Ba b of b, ... form used above to Faa di Bruno (1855) Proof The proof of this goes roughly as follows The in nite Taylor development of the composition is the composition of the Taylor developments, j (f g)(x) ... Invariant theory of compact Lie groups, 3.8 17 3.8 Corollary Under the same conditions as 3.7: : C0 (Rk ) ; C0 (V )G ! is surjective, where C0 denotes the space of all germs at of C Proof C (V )G...

Ngày tải lên: 31/03/2014, 16:18

... class groups of algebraic groups 8.1 Class numbers of algebraic groups and number of classes in a genus 8.2 Class numbers and class groups of semisimple groups of ... structure of groups of rational points of anisotropic groups and the multiplicative arithmetic of skew fields, which use most of the machinery developed in the arithmetic theory of algebraic groups ... One of the primary research tools for the arithmetic theory of algebraic groups is adele groups, whose properties are studied in Chapter The primary focus of Chapter is a complete proof of the...

Ngày tải lên: 31/03/2014, 16:21

Ngày tải lên: 13/05/2014, 12:22

... Appendix E COMPLEXES OF GROUPS E.1 E.2 E.3 Background on Graphs of Groups Complexes of Groups The Meyer-Vietoris Spectral Sequence Appendix F HOMOLOGY AND COHOMOLOGY OF GROUPS F.1 F.2 F.3 F.4 ... Group Ring Coefficients Background on the Ends of a Group The Ends of W Splittings of Coxeter Groups Cohomology of Normalizers of Spherical Special Subgroups Chapter THE FUNDAMENTAL GROUP AND THE ... Reflection Groups Finite groups generated by orthogonal linear reflections on Rn play a decisive role in • the classification of Lie groups and Lie algebras; • the theory of algebraic groups, as...

Ngày tải lên: 11/06/2014, 13:33

Ngày tải lên: 12/06/2014, 16:08

Ngày tải lên: 05/08/2014, 15:21

... embedding of) nX from X[Y ] The Cayley Graph of Abelian Groups with Valency at Most Four Let Γ = Cay(G, S) be a connected undirected Cayley graph of an abelian group G on S, with the valency of Γ ... which graphs in the lists are normal edge-transitive The proof of Theorem 1.2 is in Secs and We consider the Cayley graph of abelian groups with valency at most four in Sec and with valency in ... |S| ≤ 4 Edge-Transitive Cayley Graph of Abelian Groups with Valency Five Our purpose in this section is to show all edge-transitive Cayley graphs of abelian groups with valency five which are not...

Ngày tải lên: 06/08/2014, 05:20

... subspace of V , say of co-dimension c, such that the union of all images of W under τ covers all elements of V Then G acts transitively on the set W \G of right cosets of W in G (of size kpc ) by ... objects arise as orbits of Singer groups or subgroups of Singer groups It seems, however, that only point (and, in the case the electronic journal of combinatorics (2002), #R15 of [9], line) orbits ... spread of Σn−1 This flat is therefore filled by S (as in the proof of Lemma 2.2), so X is a (d/u − 1)-flat of the P G(n/u − 1, q u ) corresponding to S Now the orbit of X as a (d − 1)-flat of P G(n...

Ngày tải lên: 07/08/2014, 06:23

... of partitions of n The number p∗ (n) of regular partitions of n equals the number of class regular partitions of n and then p (n) = p(n) − p∗ (n) is the number of (class)singular partitions of ... (µ,i,j)∈T where as above j is the -part of j Thus bcreg /acreg = c , where c is the sum of n n the exponents of the powers v of , occuring as factors in the integers of the product µ class,i≥1 mi (µ)! ... all regular classes Proof of Theorem 2: The matrix form of (1) above may be stated as reg Y n = Dn X n , where Yn is the p(n) × p∗ (n)-submatrix of Xn containing the values of all irreducible characters...

Ngày tải lên: 07/08/2014, 07:21

... family of subsets The proof of Lemma 3.5 given in [4] can be easily modified to yield a similar result for G For the convenience of the reader, we include the proof below the electronic journal of ... the required shape as above Proof of Theorem 1.4 As before, the upper bound of |I| is given by the existence of Latin squares of order n1 and Latin rectangles of order n1 × ni for all n1 < ni ... #R25 Proof of Theorem 2.1 We shall imitate the proof of Theorem 4.2 in [8] by Larose and Malvenuto For the argument to work for even permutations, we require a slightly greater degree of freedom,...

Ngày tải lên: 07/08/2014, 15:22