The Plancherel Formula, the Plancherel Theorem, and the Fourier transform of orbital integrals

We discuss various forms of the Plancherel Formula and the Plancherel Theorem on reductive groups over local fields.

[1]  V. Bargmann,et al.  Irreducible unitary representations of the Lorentz group , 1947 .

[2]  F. I. Mautner UNITARY REPRESENTATIONS OF LOCALLY COMPACT GROUPS II , 1950 .

[3]  I. Segal AN EXTENSION OF PLANCHEREL'S FORMULA TO SEPARABLE UNIMODULAR GROUPS , 1950 .

[4]  Harish-Chandra Plancherel Formula for the 2 x 2 Real Unimodular Group. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[5]  F. Bruhat Sur les Representations des Groups Classiques -Adiques II , 1961 .

[6]  I. Satake On Spherical Functions over p-adic Fields , 1962 .

[7]  I. Satake,et al.  Theory of spherical functions on reductive algebraic groups over p-adic fields , 1963 .

[8]  Harish-Chandra Discrete series for semisimple Lie groups I , 1965 .

[9]  Harish-Chandra Two Theorems on Semi-simple Lie Groups , 1966 .

[10]  P. Sally,et al.  Special functions on locally compact fields , 1966 .

[11]  P. Sally,et al.  Characters of the discrete series of representations of sl(2) over a local field. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Sally Pj,et al.  Characters of the discrete series of representations of sl(2) over a local field. , 1968 .

[13]  Spherical functions on a $\mathfrak{p}$-adic Chevalley group , 1968 .

[14]  T. Shintani On certain square-integrable irreducible unitary representations of some p-adic linear groups , 1968 .

[15]  P. Sally,et al.  The plancherel formula for sl(2) over a local field. , 1969, Proceedings of the National Academy of Sciences of the United States of America.

[16]  J. Preuner Harmonic analysis on reductive p-adic groups , 1974 .

[17]  Some applications of the Schwartz space of a semisimple Lie group , 1970 .

[18]  Automorphic Forms on GL(2) , 1970 .

[19]  Harish-Chandra Harmonic analysis on semisimple Lie groups , 1970 .

[20]  A. Silberger PGL2 over the p-adics. Its Representations, Spherical Functions, and Fourier Analysis , 1970 .

[21]  R. Rao Orbital Integrals in Reductive Groups , 1972 .

[22]  On the theory of the Eisenstein integral , 1972 .

[23]  J. Shalika A Theorem on Semi-Simple P-adic Groups , 1972 .

[24]  Commutativity of intertwining operators. II , 1973 .

[25]  P. Sally,et al.  The fourier transform on semisimple lie groups of real rank one , 1973 .

[26]  L. Corwin Representations of division algebras over local fields , 1974 .

[27]  J. Preuner Harmonic analysis on real reductive groups I the theory of the constant term , 1975 .

[28]  W. Schmid On the characters of the discrete series , 1975 .

[29]  Invariant eigendistributions of Laplace operators on real simple Lie groups, III: Methods of construction for semisimple Lie groups , 1976 .

[30]  Harish-Chandra Harmonic Analysis on Real Reductive Groups III. The Maass-Selberg Relations and the Plancherel Formula , 1976 .

[31]  Harish-Chandra Harmonic analysis on real reductive groups. II , 1976 .

[32]  A. W. Knapp,et al.  Classification of irreducible tempered representations of semisimple Lie groups. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[33]  G. Zuckerman Tensor products of finite and infinite dimensional representations of semisimple Lie groups , 1977 .

[34]  V. Varadarajan Harmonic analysis on real reductive groups , 1977 .

[35]  Singular invariant eigendistributions as characters , 1977 .

[36]  R. Howe Tamely ramified supercuspidal representations of ${\rm Gl}_{n}$. , 1977 .

[37]  R. Herb Fourier inversion of invariant integrals on semisimple real Lie groups , 1979 .

[38]  R. Herb,et al.  Singular invariant eigendistributions as characters in the fourier transform of invariant distributions , 1979 .

[39]  R. Herb,et al.  Fourier inversion and the plancherel theorem , 1981 .

[40]  Fourier Inversion and the Plancherel Theorem for Semisimple Real Lie Groups , 1982 .

[41]  P. Sally,et al.  The fourier transform of orbital integrals on SL 2 over a p-adic field , 1983 .

[42]  R. Herb Discrete series characters and Fourier inversion on semisimple real Lie groups , 1983 .

[43]  Harish-Chandra Supertempered Distributions on Real Reductive Groups , 1984 .

[44]  F. Shahidi Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n) , 1984 .

[45]  A. Moy Local Constants and the Tame Langlands Correspondence , 1986 .

[46]  P. Sally Some Remarks on Discrete Series Characters for Reductive p-adic Groups , 1988 .

[47]  L. Corwin The unitary dual for the multiplicative group of arbitrary division algebras over local fields , 1989 .

[48]  F. Shahidi A proof of Langland’s conjecture on Plancherel measures; Complementary series of $p$-adic groups , 1990 .

[49]  L. Morris Tamely ramified supercuspidal representations of classical groups. I. Filtrations , 1991 .

[50]  L. Morris Tamely ramified supercuspidal representations of classical groups. II. Representation theory , 1992 .

[51]  Elliptic representations for Sp(2n) and SO(n) , 1993 .

[52]  J. Arthur On elliptic tempered characters , 1993 .

[53]  C. Bushnell,et al.  The admissible dual of GL(N) via compact open subgroups , 1993 .

[54]  A. Silberger,et al.  Some consequences of Harish-Chandra’s submersion principle , 1993 .

[55]  R. Herb Supertempered virtual characters , 1994 .

[56]  J. Arthur On the Fourier transforms of weighted orbital integrals. , 1994 .

[57]  A. Moy,et al.  Unrefined minimal K-types forp-adic groups , 1994 .

[58]  G. Folland A course in abstract harmonic analysis , 1995 .

[59]  F. Murnaghan Local character expansions and Shalika germs for GL(n) , 1996 .

[60]  Harish-Chandra’s Plancherel theorem for \frak-adic groups , 1996 .

[61]  F. Murnaghan Characters of supercuspidal representations of classical groups , 1996 .

[62]  A. Silberger HARISH-CHANDRA’S PLANCHEREL THEOREM FOR p-ADIC GROUPS , 1996 .

[63]  A. Moy,et al.  Jacquet functors and unrefined minimal K-types , 1996 .

[64]  R. Herb Discrete series characters and two-structures , 1998 .

[65]  J. Adler REFINED ANISOTROPIC K-TYPES AND SUPERCUSPIDAL REPRESENTATIONS , 1998 .

[66]  J. Pantoja,et al.  Character formulas for supercuspidal representations of the groups GL 2,SL 2 , 1998 .

[67]  Correction to “Harish-Chandra’s Plancherel theorem for -adic groups” , 1999 .

[68]  P. Sally,et al.  Admissible Invariant Distributions on Reductive P-ADIC Groups , 1999 .

[69]  J. Yu Construction of tame supercuspidal representations , 2001 .

[70]  J. Waldspurger Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés , 2001 .

[71]  M. Tadic,et al.  Construction of discrete series for classical p-adic groups , 2002 .

[72]  Stephen DeBacker,et al.  Homogeneity results for invariant distributions of a reductive p-adic group , 2002 .

[73]  Plancherel measure for GL(n,F) and GL(m,D): explicit formulas and Bernstein decomposition , 2003, math/0302169.

[74]  A. Aubert,et al.  Explicit Plancherel formula for the p-adic group GL(n) , 2003 .

[75]  J. Waldspurger LA FORMULE DE PLANCHEREL POUR LES GROUPES p-ADIQUES. D’APRÈS HARISH-CHANDRA , 2003, Journal of the Institute of Mathematics of Jussieu.

[76]  Loren Spice Supercuspidal characters of SLℓ over a p-adic field, ℓ a prime , 2005 .

[77]  S. Stevens The supercuspidal representations of p-adic classical groups , 2006, math/0607622.

[78]  Ju-lee Kim Supercuspidal representations: An exhaustion theorem , 2006, math/0607262.

[79]  Loren Spice,et al.  Supercuspidal characters of reductive p-adic groups , 2007, 0707.3313.

[80]  COMMUTATIVITY OF INTERTWINING OPERATORS , 2007 .

[81]  L. Morris,et al.  Explicit Plancherel Theorems for H(q1, q2) and SL2(F) , 2009 .

[82]  Clifton Cunningham,et al.  Motivic Proof of a Character Formula for SL(2) , 2009, Exp. Math..

[83]  Stephen DeBacker,et al.  Depth-zero supercuspidal L-packets and their stability , 2009 .