Author : Yasuro Gon
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 32,56 MB
Release : 2002
Category : Mathematics
ISBN : 0821827634
Obtains an explicit formula for generalized Whittaker functions and multiplicity one theorem for all discrete series representations of $SU(2,2)$.
Author : Yasuro Gon
Publisher :
Page : 116 pages
File Size : 50,94 MB
Release : 2014-09-11
Category : Coulomb functions
ISBN : 9781470403317
Obtains an explicit formula for generalized Whittaker functions and multiplicity one theorem for all discrete series representations of $SU(2,2)$.
Author : Peter Niemann
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 27,28 MB
Release : 2002
Category : Mathematics
ISBN : 0821828886
Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.
Author : Edward L. Green
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 46,74 MB
Release : 2002
Category : Mathematics
ISBN : 0821829343
Koszul rings are graded rings which have played an important role in algebraic topology, noncommutative algebraic geometry and in the theory of quantum groups. One aspect of the theory is to compare the module theory for a Koszul ring and its Koszul dual. There are dualities between subcategories of graded modules; the Koszul modules.
Author : Robert Denk
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 11,41 MB
Release : 2003
Category : Mathematics
ISBN : 0821833782
The property of maximal $L_p$-regularity for parabolic evolution equations is investigated via the concept of $\mathcal R$-sectorial operators and operator-valued Fourier multipliers. As application, we consider the $L_q$-realization of an elliptic boundary value problem of order $2m$ with operator-valued coefficients subject to general boundary conditions. We show that there is maximal $L_p$-$L_q$-regularity for the solution of the associated Cauchy problem provided the top order coefficients are bounded and uniformly continuous.
Author : Bruce Normansell Allison
Publisher : American Mathematical Soc.
Page : 175 pages
File Size : 17,42 MB
Release : 2002
Category : Mathematics
ISBN : 0821828118
Introduction The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra, $r\ge 3$ (excluding type $\mathrm{D}_3)$ Models for $\mathrm{BC}_r$-graded Lie algebras, $r\ge 3$ (excluding type $\mathrm{D}_3)$ The $\mathfrak{g}$-module decomposition of a $\mathrm{BC}_r$-graded Lie algebra with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Central extensions, derivations and invariant forms Models of $\mathrm{BC}_r$-graded Lie algebras with grading subalgebra of type $\mathrm{B}_2$, $\mathrm{C}_2$, $\mathrm{D}_2$, or $\mathrm{D}_3$ Appendix: Peirce decompositions in structurable algebras References.
Author : Masaki Izumi
Publisher : American Mathematical Soc.
Page : 215 pages
File Size : 17,76 MB
Release : 2002
Category : Mathematics
ISBN : 0821829351
This title deals with a map $\alpha$ from a finite group $G$ into the automorphism group $Aut({\mathcal L})$ of a factor ${\mathcal L}$ satisfying (i) $G=N \rtimes H$ is a semi-direct product, (ii) the induced map $g \in G \to [\alpha_g] \in Out({\mathcal L})=Aut({\mathcal L})/Int({\mathcal L})$ is an injective homomorphism, and (iii) the restrictions $\alpha \! \! \mid_N, \alpha \! \! \mid_H$ are genuine actions of the subgroups on the factor ${\mathcal L}$. The pair ${\mathcal M}={\mathcal L} \rtimes_{\alpha} H \supseteq {\mathcal N}={\mathcal L} DEGREES{\alpha\mid_N}$ (of the crossed product ${\mathcal L} \rtimes_{\alpha} H$ and the fixed-point algebra ${\mathcal L} DEGREES{\alpha\mid_N}$) gives an irreducible inclusion of factors with Jones index $\# G$. The inclusion ${\mathcal M} \supseteq {\mathcal N}$ is of depth $2$ and hence known to correspond to a Kac algebra of dim
Author : Roger Chalkley
Publisher : American Mathematical Soc.
Page : 223 pages
File Size : 43,68 MB
Release : 2002
Category : Mathematics
ISBN : 0821827812
Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.
Author : Masaaki Furusawa
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 10,20 MB
Release : 2003
Category : Mathematics
ISBN : 0821833286
Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].
Author : Helge Glöckner
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 41,2 MB
Release : 2003
Category : Mathematics
ISBN : 0821832565
A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.
