Download Enright-Shelton Theory and Vogan's Problem for Generalized by Brian D. Boe PDF

April 4, 2017 | Science Mathematics | By admin | 0 Comments

By Brian D. Boe

This booklet investigates the composition sequence of generalized vital sequence representations brought on from a maximal cuspidal parabolic subgroup of a true reductive Lie workforce. Boe and Collingwood examine whilst such representations are multiplicity-free (Vogan's challenge #3) and the matter of describing their composition elements in closed shape. the consequences received are strikingly just like these of Enright and Shelton for optimum weight modules. Connections with diversified flag sort decompositions are mentioned.

Show description

Read or Download Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series PDF

Similar science & mathematics books


1m vorliegenden Bueh werden wir uns mit der Differentialgeometrie der Kurven und Flaehen im dreidimensionalen Raum besehiiftigen [2, 7]. Wir werden dabei besonderes Gewieht darauf legen, einen "ansehauliehen" Einbliek in die differentialgeometrisehen Begriffe und Satze zu gewinnen. Zu dies em Zweek werden wir, soweit sieh dies in naheliegender Weise er mogliehen lal3t, den differentialgeometrisehen Objekten elementargeome trisehe oder, wie wir dafiir aueh sagen wollen, differenzengeometrisehe Modelle gegeniiberstellen und deren elementargeometrisehe Eigensehaften mit differentialgeometrisehen Eigensehaften der Kurven und Flaehen in Be ziehung bringen.

Elements of the History of Mathematics

This paintings gathers jointly, with no big amendment, the key­ ity of the ancient Notes that have looked as if it would date in my parts de M atMmatique. simply the move has been made self reliant of the weather to which those Notes have been hooked up; they're for this reason, in precept, available to each reader who possesses a valid classical mathematical history, of undergraduate ordinary.

Zero : a landmark discovery, the dreadful void, and the ultimate mind

0 shows the absence of a volume or a significance. it's so deeply rooted in our psyche this present day that no-one will most likely ask "What is 0? " From the start of the very construction of existence, the sensation of loss of whatever or the imaginative and prescient of emptiness/void has been embedded by way of the author in all dwelling beings.

Additional info for Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series

Example text

J - i is odd. \ € ftp. 7), e = par^(e i + 1 - ek) = par*(ej - e,_ 1) = -/x. D The next several results provide specific information about the correspondence between sets ft € £s and subsets ( S * ^ . These results will be crucial for proving that the composition factors of TT(8) occur without multiplicities. We begin by showing that ft+ uniquely determines ft. 10. Given 8 e P™ax and a subset G C $ + , there exists at most one ft G £$ such that ft j = 0 . PROPOSITION Proof. Suppose such an ft exists.

5 p + 1 X % ) ) . 19a) V0 = VG U VPn U P P n _ 1 U VPrn, leading to parameters of types 2* in T>G\ (i,j) and (z,j) in Vpn\ i in Dp n _jj (i,j)* and (2,j) b i n P P m . 19b) S = {1*} U {(0, j) | 1 < j < 2n - 2} is in one-to-one correspondence with the diagram W^ with its longest element removed. )• Lot V$ denote the totality of Qtt-orbit or K-orbit parameters attached to S in this way. ,„-1)1 } 44 BRIAN D. BOE AND DAVID H. COLLINGWOOD We can arrange things so that 6\+ indexes the holomorphic discrete series representation in HC0.

3, consider the set S' consisting of all z e Phoio,M such that (1,2) ^ z :< (n - l,n) . 22b) S = S'u{l}. Then S parametrizes a small part of the Hermitian symmetric poset W^ attached to the pair (D n , An-\). )• Let P 5 denote the totality of Q^-orbit or K-orbit parameters attached to S in this way. 4): wi if 2 < j < n, = Si] 48 BRIAN D. BOE AND DAVID H. COLLINGWOOD if 3 < j < n, 2

Download PDF sample

Rated 4.67 of 5 – based on 22 votes