algebraic groups and discontinuous subgroups

Ngày tải lên: 27/03/2014, 11:48

... ~('1, for i > 1, and Uo = UD = 0; and Co = D('). It follows from (1.16) that Ui and Ci are normal subgroups of D* (called the congruence subgroups of D and D(') respectively, ... Since UD and D(') are clearly compact groups, and Ui and Ci are open in UD and D(') respectively (and, moreover, generate a base of neighborhoods...

Ngày tải lên: 31/03/2014, 16:21

... Geometric Langlands duality and representations of algebraic groups over commutative rings By I. Mirkovi´c and K. Vilonen* LANGLANDS DUALITY AND ALGEBRAIC GROUPS] 113 We will now ... LANGLANDS DUALITY AND ALGEBRAIC GROUPS] 103 but (g K ) −ψ does. We conclude that for the SL 2 -subgroup generated by the one parameter subgroups U ±ψ the orbit through L ν is a...

Ngày tải lên: 06/03/2014, 08:21

... your_username and open your_firstname Console. b. Expand Northwind Traders (Exchange), expand Servers, and then expand your_servername. c. Right-click your_servername, point to New, and then ... point to Programs, point to Accessories, and then click Windows Explorer. b. Expand My Computer, expand Local Disk (D:), expand Program Files, and then expand Exchsrvr to view the...

Ngày tải lên: 21/12/2013, 05:18

... weight of the standard representation of GL(r − 1), and c(λ)=1+(a 1 − a 2 ).(6) Both λ  and λ  are the highest weights of some GL(r − 1) irreducible modules. (Note: 0  = 0.) Expanding S λ as ... =((n − 1)a, (n − 2)a, ,a,0) and λ =((n − 1)b, (n − 2)b, . . . , b, 0), for some positive integers k, a, b. Then the characters can be expanded as Vandermonde determinants and we have, S...

Ngày tải lên: 14/03/2014, 22:20

... hydroxyl (OH) group, and aldehydes, ketones are characterized by carbonyl groups (C=O). There are various combinations of hydroxyl groups in molecules along with carbonyl groups and these combinations ... 1 Functional Groups and Chemical Families Although there are a wide variety of organic compounds, most of them are composed of the elements from the upper right hand portion of...

Ngày tải lên: 22/03/2014, 14:20

... injection. 4.1.6. Let C, C  , D and D  be four categories, G : C→C  , G ∨ : C  →C, H : D→D  and H ∨ : D  →D, and (G, G ∨ ) and (H, H ∨ ) be two adjoint pairs. Let F : C→Dand F  : C  →D  be two ... under extensions and direct summands and containing E i T for all i ≥ 0 and T a simple object of A such that FT = 0. Then, in general, not every projective object of A is in F...

Ngày tải lên: 29/03/2014, 07:20

... Classical Real Analysis R. Salem, Algebraic Numbers and Fourier Analysis, and L. Carleson, Selected Problems on Exceptional Sets ALGEBRAIC NUMBERS AND FOURIER ANALYSIS . RAPHAEL SALEM ... distinct real zeros between -2 and +2. The equation has then m - I real roots (algebraic integers) between -2 and +2, and one real root between r and r + em (em...

Ngày tải lên: 31/03/2014, 15:08

... of rotations, and generalizations thereof, will play a central role in subsequent lectures. L.1.5 11 Lecture 2: Lie Groups and Lie Algebras Lie Groups. In this lecture, I define and develop some ... the group “multiplication” is taken to be addition. Example: Matrix Lie Groups. The Lie subgroups of GL(n, R)arecalled matrix Lie groups and play an important role in the theory. No...

Ngày tải lên: 31/03/2014, 16:15

... Exercise 7. 2.7. The symplectic groups Sp(n; R), Sp(n; C),andSp(n). The special and general linear groups, the orthogonal and unitary groups, and the symplectic groups (which will be defined momentarily) ... following groups also violate (2), and hence are non-compact: O(n; C )and SO(n; C); O(n; k)andSO(n; k)(n ≥ 1, k ≥ 1); the Heisenberg group H; Sp (n; R) and Sp (n; C); E(...

Ngày tải lên: 31/03/2014, 16:18