Calculations in Algebraic Groups and their consequences
The economic consequences of extending the use of fair value accounting in regulatory capital calculations
... 4 market reactions to events that increase (decrease) the likelihood of inclusion of AFS fair value gains and losses in regulatory capital. A key challenge of examining the economic consequences of any regulation ...
54
CALCULATIONS IN COXETER GROUPS
... ane groups of type A n was described implicitly in [Shi 1984] in quite another ...general groups. At any rate, there ought to be some interesting consequences of the niteness of the automaton ...
24
The irreducible subgroups of exceptional algebraic groups
... tional algebraic groups over algebraically closed fields of arbitrary ...semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of ...exceptional ...
197
Finite Simple Subgroups of Exceptional Algebraic Groups
... simple groups / ∈ Lie(p), the so-called non-generic case, we have two problems: which such simple groups embed into G, and how do they embed? For example, are there any Lie primitive embeddings? If not, ...
248
Simple irreducible subgroups of exceptional algebraic groups
... semisimple algebraic group is called irreducible if it lies in no proper parabolic ...exceptional algebraic groups G which are connected, closed and simple of rank at least ...2. Consequences ...
47
A note on the tensor product of restricted simple modules for algebraic groups
... L(1, 1) ⊗ L(1, 1) ∼ = T (2, 2) ⊕ 2St where T (2, 2) has G 1 -socle k. Type B 2 = C 2 , p = 2: Choose the following ordering on the set of simple roots: hα 1 , α ˇ 2 i = −1 and hα 2 , α ˇ 1 i = −2. Note that all ...
17
Algebraic Envelope of Groups and their Properties
... texts written by Milne [Mil12] and Waterhouse [Wat12] are the main references I used for these two chapters, although both of them mainly focused on affine group schemes. At the start of chapter 3 we will show an ...
92
Linear algebraic groups, with special emphasis on the classical groups
... Classical Groups are examples of semisimple ...Reductive groups have a particularly elegant structure theory, which we present in all its glory in ...reductive groups are more convenient to work with ...
224
On the automorphism groups of algebraic bounded domains
... subvariety V ′ ⊂ V the variety V defines f and f −1 as possibly multiple-valued algebraic maps. Since dim C V = n, dim C V ′ ≤ n − 1. Since dim R H 1 = 2n − 1, there exists a point x ∈ H 1 ∩ U 1 and a neighborhood ...
29
Reducible subgroups of exceptional algebraic groups
... linear algebraic groups is a theory with applications throughout alge- bra and ...Lie groups give direct applications in geometry and ...simple groups, for instance the subgroup structure of ...
48
Amenability and coamenability of algebraic quantum groups
... - algebraic quantum group theory but those parts of their theory that are most relevant are scattered throughout the literature and are often presented only in a very sketchy ...
25
On linear algebraic groups over pseudoglobal fields
... Proof of Theorem 3. Note, that the proof of this theorem is carried out by the argument analogous to used in the case of a number ground field. First we show, that all the group indicated in the statement of Theorem 3 are ...
12
On the modular representation theory of algebraic Chevalley groups
... Verma : Role of Affine Weyl Groups ; in the Representation Theory of Algebraic ' Chevalley Groups; and their Lie-Algebras,.. Proc.[r] ...
71
Tannakian Categories and Linear Differential Algebraic Groups
... linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful ...differential algebraic groups by introducing a category corresponding to their ...
87
Irreducible A1 subgroups of exceptional algebraic groups
... Corollary 1. Let G be an exceptional algebraic group. Then G contains an irreducible subgroup A 1 , unless G = E 6 and p = 2. Given the existence of irreducible A 1 subgroups, we can use the proofs of Theorems 2 ...
52
Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
... [33] Marquette I and Quesne C 2015 Deformed oscilator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational ex- tensions J. Math. Phys. 56, 062102. [34] Fris I, ...
21
On non-generic finite subgroups of exceptional algebraic groups
... 2010 Mathematics Subject Classification. Primary 20G15, 20E07. Key words and phrases. algebraic groups, exceptional groups, finite simple groups, Lie primitive, subgroup structure, complete ...
162
Explicit calculations of automorphic forms for definite unitary groups
... C(x, y) = (x 2 + y 2 ) 2 − 8x(x 2 − 3y 2 ) + 18(x 2 + y 2 ) − 27 6 0. In this case we find that C(x, y) = − 56727 4096 , so the condition is satisfied. 5. Some higher level examples We shall now introduce some level ...
17
ALGEBRAIC SURFACES WITH LOG CANONICAL SINGULARITIES AND THE FUNDAMENTAL GROUPS OF THEIR SMOOTH PARTS
... for the definition of log canonical singularity and to [4] or [6] for a complete list of log canonical singularities with reduced boundary. Theorem (2.3). Let S be a normal projective algebraic surface with at ...
10
Isomorphy Classes of k-involutions of Algebraic Groups of Type G2 and F4.
... Since, groups of type G 2 are automorphism groups of an octonion algebra, many aspects of their structure can be revealed by the structure of the ...
191