Harmonic analysis, group representations, automorphic forms, by Jian-Shu Li, Eng-Chye Tan, Nolan R Wallach, Chen-Bo Zhu

By Jian-Shu Li, Eng-Chye Tan, Nolan R Wallach, Chen-Bo Zhu

This quantity incorporates an identical identify as that of a global convention held on the nationwide collage of Singapore, Sep 11 January 2006 at the celebration of Roger E. Howe's sixtieth birthday. Authored by means of prime contributors of the Lie concept group, those contributions, extended from invited lectures given on the convention, are a becoming tribute to the originality, intensity and impression of Howe's mathematical paintings. the variety and variety of the subjects will entice a extensive viewers of study mathematicians and graduate scholars attracted to symmetry and its profound functions.

Show description

By Jian-Shu Li, Eng-Chye Tan, Nolan R Wallach, Chen-Bo Zhu

This quantity incorporates an identical identify as that of a global convention held on the nationwide collage of Singapore, Sep 11 January 2006 at the celebration of Roger E. Howe's sixtieth birthday. Authored by means of prime contributors of the Lie concept group, those contributions, extended from invited lectures given on the convention, are a becoming tribute to the originality, intensity and impression of Howe's mathematical paintings. the variety and variety of the subjects will entice a extensive viewers of study mathematicians and graduate scholars attracted to symmetry and its profound functions.

Show description

Read or Download Harmonic analysis, group representations, automorphic forms, and invariant theory: in honor of Roger E. Howe PDF

Best symmetry and group books

Von Zahlen und Größen: dritthalbtausend Jahre Theorie und Praxis 2

Dieses zweib? ndige Werk handelt von Mathematik und ihrer Geschichte. Die sorgf? ltige examine dessen, was once die Alten bewiesen - meist sehr viel mehr, als sie ahnten -, f? hrt zu einem besseren Verst? ndnis der Geschichte und zu einer guten Motivation und einem ebenfalls besseren Verst? ndnis heutiger Mathematik.

Großgruppenverfahren: Lebendig lernen - Veränderung gestalten (German Edition)

Organisationen und ihre Mitarbeiter m? ssen fortlaufend lernen und sich ver? ndern, um konkurrenzf? hig zu bleiben. Eine effektive M? glichkeit, Ver? nderungsprozesse in Unternehmen zu steuern, stellen Gro? gruppenverfahren dar, denn sie binden auf strukturierte und transparente Weise viele Menschen in einen gemeinsamen Prozess ein.

Extra resources for Harmonic analysis, group representations, automorphic forms, and invariant theory: in honor of Roger E. Howe

Example text

Cm , 0, . . , 0, d1 , . . , dn )+ 1 (r − s, . . , r − s; s − r, . . , s − r) → 2 σ = (a1 , . . , ak , 0, . . , 0, d1 , . . , dn ; c1 , . . , cm , 0, . . , 0, b1 , . . , b )+ 1 (p − q, . . , p − q; q − p, . . , q − p) 2 where the obvious inequalities hold: k + ≤ p, m + n ≤ q, k + n ≤ r, m + ≤ s III. (G, G ) = (Sp(p, q), O ∗ (2n)), (K, K ) = (Sp(p) × Sp(q), U (n)). (a1 , . . , ar , 0, . . , 0; b1 , . . , bs , 0, . . , 0) → (a1 , . . , ar , 0, . . , 0, −b1 , . . , −bs ) + (p − q, .

Finally (O(p, q), Sp(2nR)) witih p + q = 2n + 1 is in [4], this is similar to [33] except that the covering groups are unavoidable. We first consider the case p, q even. In this case the covering of Sp(2n, R) splits and the correspondence can be written in terms of the linear groups. Roughly speaking the correspondence in these cases is “functorial”, and a number of nice properties hold which fail in general. In particular the minimal K–type in the sense of Vogan is always of minimal degree in this situation.

Ak , 0, . . , 0; ) 1− 2 Sp(2n, R) : (p−2k) p p p p p p τ = (a1 + , . . , ak + , + 1, . . , + 1, , . . , ) . 2 2 2 2 2 2 All such highest weights occur, subject to the constraints k ≤ [ p2 ] and k + 1− 2 (p − 2k) ≤ n. 20 Jeffrey Adams This means that the weight σ for O(p) is the highest weight of the irreducible representation σ, and the weight for Sp(2n, R) is the highest weight of the K –type of τ of lowest degree in π . II. (U (p), U (m, n)) The inverse image K of U (p) in Sp(2p(m + n), R) is isomorphic to the p m+n cover defined by the character det 2 .

Download PDF sample

Rated 4.06 of 5 – based on 45 votes