By Jian-Shu Li, Eng-Chye Tan, Nolan R Wallach, Chen-Bo Zhu
This quantity includes a similar identify as that of a world convention held on the nationwide collage of Singapore, September 11 January 2006 at the celebration of Roger E. Howe's sixtieth birthday. Authored via top contributors of the Lie concept group, those contributions, elevated 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 vast viewers of study mathematicians and graduate scholars drawn to symmetry and its profound functions.
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Publication by way of Dicks, W.
The idea that of symmetry is inherent to trendy technological know-how, and its evolution has a posh background that richly exemplifies the dynamics of medical swap. This learn relies on basic resources, offered in context: the authors learn heavily the trajectory of the idea that within the mathematical and medical disciplines in addition to its trajectory in paintings and structure.
Additional resources for Harmonic analysis, group representations, automorphic forms, and invariant theory: in honor of Roger E. Howe
We assume, as is often the 26 Jeffrey Adams case, that (M, M ) is itself a dual pair in some Sp(2m, R). Let ω be an oscillator representation for Sp(2n, R) restricted to G × G , and let ωM be an oscillator representation for M × M . The Jacquet module ωN ×N of ω is a representation of M × M , and a calculation shows it has ωM ζ as a quotient for some character ζ of M × M . Suppose there is a non–zero M × M map ˇ φ : ωM → σ ⊗σ for some representation σ ⊗ σ of M × M . That is θ(ψ, M, M )(σ) = σ .
2q + τ ) + 2). Example 8. (O(p, q), Sp(2n, R)) with p + q = 2n, 2n + 1, 2n + 2. In these examples the groups are the same “size”, and are of particular interest from the point of view of L–functions (cf. the lectures of Steve Kudla). This is the opposite extreme of the stable range . ). The cases (O(p, q), Sp(2n, R)) with p + q = 2n, 2n + 2 and p, q even are in , p, q odd are only missing because of covering group technicalities. Finally (O(p, q), Sp(2nR)) witih p + q = 2n + 1 is in , this is similar to  except that the covering groups are unavoidable.
Pages 179– 207. Amer. Math. , Providence, RI, 1985.  Roger Howe. The oscillator semigroup. In The mathematical heritage of Hermann Weyl (Durham, NC, 1987), volume 48 of Proc. Sympos. , pages 61–132. Amer. Math. , Providence, RI, 1988. The Theta Correspondence over R 37  Roger Howe. Remarks on classical invariant theory. Trans. Amer. Math. , 313(2):539–570, 1989.  Roger Howe. Transcending classical invariant theory. J. Amer. Math. , 2(3):535–552, 1989.  Roger Howe. Perspectives on invariant theory: Schur duality, multiplicityfree actions and beyond.