Representations of semisimple Lie groups

@inproceedings{Knapp2000RepresentationsOS,
  title={Representations of semisimple Lie groups},
  author={Anthony W. Knapp and Peter E. Trapa},
  year={2000}
}
We keep to the notation of the preceding note.1 Since mo is reductive, there will be no essential loss of generality from the point of view of irreducible unitary representations of Mo if we assume that mo is semisimple. Then ma n f0 is a maximal compact subalgebra of MO, and bfo is a Cartan subalgebra of mo. Moreover, mo = mo n to + mo n po. Our problem of constructing irreducible unitary representations of Mo is therefore the same as that for G, under the additional assumption that a maximal… 
REPRESENTATIONS OF SEMISIMPLE LIE GROUPS
positive compact roots. The Killing form of go induces an inner product (, ) on hR*. We introduce an integer-valued function Q on A: Q(,) is the number of distinct ways in which u can be expressed as
Dimension of the space of intertwining operators from degenerate principal series representations
Let X be a homogeneous space of a real reductive Lie group G. It was proved by T. Kobayashi and T. Oshima that the regular representation $$C^{\infty }(X)$$C∞(X) contains each irreducible
GEOMETRIC CYCLES IN COMPACT LOCALLY HERMITIAN SYMMETRIC SPACES AND AUTOMORPHIC REPRESENTATIONS
Let G be a linear connected non-compact real simple Lie group and let K ⊂ G be a maximal compact subgroup of G. Suppose that the centre of K is isomorphic to 𝕊1 so that X := G/K is a global
Unitary representations of real reductive groups
We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits
The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups
For complex reductive Lie algebras g, the classical Harish-Chandra homomorphism allows to link irreducible finite dimensional representations of g to those of certain subalgebras r. The
Relationship between orbit decomposition on the flag varieties and multiplicities of induced representations
  • T. Tauchi
  • Mathematics
    Proceedings of the Japan Academy, Series A, Mathematical Sciences
  • 2019
Let G be a real reductive Lie group and H a closed subgroup. T. Kobayashi and T. Oshima established a finiteness criterion of multiplicities of irreducible G-modules occurring in the regular
Homomorphisms and extensions of principal series representations
In this article we describe homomorphisms and extensions of principal series representations. Principal series are certain representations of a semisimple complex Lie algebra g and are objects of the
Quaternionic discrete series
This work investigates the discrete series of linear connected semisimple noncompact groups G. These are irreducible unitary representations that occur as direct summands of L2(G). Harish-Chandra
Family of D-modules and representations with a boundedness property
In the representation theory of real reductive Lie groups, many objects have finiteness properties. For example, the lengths of Verma modules and principal series representations are finite, and more
Theory ? ? ( ? ? ) ? ? { ? ? c ? ?
Let G be a connected noncompact simple Hermitian symmetric group with nite center. Let H() denote the geometric realization of an irreducible unitary highest weight representation with highest
...
...

References

SHOWING 1-10 OF 13 REFERENCES
REPRESENTATION THEORY OF SEMISIMPLE GROUPS: An Overview Based on Examples
Page 55, proof of Lemma 3.13. This proof is incorrect as it stands because it involves an interchange of limits that has not been justified. A naive attempt to fix the proof might involve assuming
Théorie des distributions
II. Differentiation II.2. Examples of differentiation. The case of one variable (n = 1). II.2.3. Pseudofunctions. Hadamard finite part. We calculate the derivative of a function f(x) which is equal
Academic press.
CONTENTS: Basic Principles, Definitions, and Units. ORD and CD of Organic Functional Groups. Solvent and Tempera­ ture Effects. Amides, Peptides, Nucleosides, Nucleotides, Pigments, and Porphyrins.
Birkhäuser
  • Boston,
  • 1996
Princeton
  • NJ,
  • 1995
1962; second edition
  • Dover Publications, New York,
  • 1979
Springer-Verlag
  • New York,
  • 1972
STEVENS AND LITTLE 6 See S
  • Bochner and W. T. Martin, Several Complex Variables (Princeton, N.J.: Princeton University Press, 1948), p. 117. 7 Our procedure for constructing i-t is a generalization of the method used by Bargmann (Ann. Math., 48, 620, 1947) and Gelfand and Graev
  • 1953
Trudi Mat
  • Inst. Steklova vol. 36
  • 1950
Princeton
  • NJ,
  • 1946
...
...