1549380232-Automorphic_Forms_and_Applications__Sarnak_

DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS 387 3) For every noncompact imaginary root (3 E II that is orthogonal to th ...

388 DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS The natural "mult iplicative" structure ExtP(A,B) 0 Extq(B,C)--+ Extp+q ...

DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS 389 a) The representation μLi is a lambda-lowest £ 1 n K-type; so it has mu ...

390 DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS ([Green], Definition 5.3.22). The construction of .>-f provides also ...

DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS 391 be taken on the same Cartan subgroup H = TA of L, with a common discret ...

392 DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS q, >-and q' , A' satisfy the hypotheses of Theorem 7, that nL is a o ...

DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS 393 ([Green], Corollary 6.3.4; here r =dim u n p ). Since the limit is non- ...

394 DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS unitary representation of G, andμ E (tc)* is an extremal weight of a re ...

DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS 395 Now the eigenvalue of the Casimir operator for G in 7r (and therefore a ...

396 DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS positive system 6. + of Theorem 10 contains the Iwasawa positive system ...

Bibliography [BD] P. Bernat and J. Dixmier, "Sur le dual d'un groupe de Lie,'' C. R. Acad. Sci. Paris 250 (1960), 1778 - 1779. [ ...

398 DAVID A. VOGAN, JR, ISOLATED UNITARY REPRESENTATIONS [Green] D. Vogan, Representations of Real Reductive Lie Groups. Birkhau ...

Ramanujan Graphs and Ramanujan Hypergraphs Wen-Ching Winnie Li ...

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IAS/Park City Mathematics Series Volume 12, 2002 Ramanujan Graphs and Ramanujan Hypergraphs Wen-Ching Winnie Li Introduction The ...

402 W.-C. W. LI, RAMANUJAN GRAPHS AND RAMANUJAN HYPERGRAPHS also eigenvalues of certain Ramanujan graphs. We end this lecture by ...

Lecture 1. Ramanujan graphs and connections with number theory 1.1. Spectral theory of regular graphs The structure of a finite ...

404 W.-C. W. LI, RAMANUJAN GRAPHS AND RAMANUJAN HYPERGRAPHS (3) [Nilli [31]]. He showed that if the diameter of a k-regular grap ...

LECTURE 1. RAMANUJAN GRAPHS 405 Again, if each x in Um+l h as one neighbor in Um and q neighbors in Um+ 2 , then Ag(x)= (~)m+q(~ ...

406 W.-C. W. LI, RAMANUJAN GRAPHS AND RAMANUJAN HYPERGRAPHS When used as communication networks, Ramanujan graphs transmit infor ...