Singularities of intertwining operators and decompositions of principal series representations

Taeuk Nam; Avner Segal; Lior Silberman

Singularities of intertwining operators and decompositions of principal series representations

Taeuk Nam, Avner Segal, Lior Silberman

Research output: Contribution to journal › Article › peer-review

Abstract

We show that, under certain assumptions, a parabolic induction Ind^G_B λ from the Borel subgroup B of a (real or p-adic) reductive group G decomposes into a direct sum of the form: Ind^G_B λ = ( Ind^G_P St_M ⊗χ₀ ) ⊕ ( Ind^G_P 1_M ⊗χ₀ ), where P is a parabolic subgroup of G with Levi subgroup M of semi-simple rank 1, 1_M is the trivial representation of M, St_M is the Steinberg representation of M and χ₀ is a certain character of M. We construct examples of this phenomenon for all simply-connected simple groups of rank at least 2.

Original language	English
Pages (from-to)	939-964
Number of pages	26
Journal	Journal of Lie Theory
Volume	30
Issue number	4
State	Published - 1 Jan 2020
Externally published	Yes

Keywords

Intertwining operators
Lie groups
P-adic groups
Principle series
Representation theory

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

@article{020d87c1d44f4d55b41b80516d659a5f,

title = "Singularities of intertwining operators and decompositions of principal series representations",

abstract = "We show that, under certain assumptions, a parabolic induction IndGB λ from the Borel subgroup B of a (real or p-adic) reductive group G decomposes into a direct sum of the form: IndGB λ = ( IndGP StM ⊗χ0 ) ⊕ ( IndGP 1M ⊗χ0 ), where P is a parabolic subgroup of G with Levi subgroup M of semi-simple rank 1, 1M is the trivial representation of M, StM is the Steinberg representation of M and χ0 is a certain character of M. We construct examples of this phenomenon for all simply-connected simple groups of rank at least 2.",

keywords = "Intertwining operators, Lie groups, P-adic groups, Principle series, Representation theory",

author = "Taeuk Nam and Avner Segal and Lior Silberman",

note = "Publisher Copyright: {\textcopyright} 2020 Heldermann Verlag",

year = "2020",

month = jan,

day = "1",

language = "English",

volume = "30",

pages = "939--964",

journal = "Journal of Lie Theory",

issn = "0949-5932",

publisher = "Heldermann Verlag",

number = "4",

}

TY - JOUR

T1 - Singularities of intertwining operators and decompositions of principal series representations

AU - Nam, Taeuk

AU - Segal, Avner

AU - Silberman, Lior

PY - 2020/1/1

Y1 - 2020/1/1

N2 - We show that, under certain assumptions, a parabolic induction IndGB λ from the Borel subgroup B of a (real or p-adic) reductive group G decomposes into a direct sum of the form: IndGB λ = ( IndGP StM ⊗χ0 ) ⊕ ( IndGP 1M ⊗χ0 ), where P is a parabolic subgroup of G with Levi subgroup M of semi-simple rank 1, 1M is the trivial representation of M, StM is the Steinberg representation of M and χ0 is a certain character of M. We construct examples of this phenomenon for all simply-connected simple groups of rank at least 2.

AB - We show that, under certain assumptions, a parabolic induction IndGB λ from the Borel subgroup B of a (real or p-adic) reductive group G decomposes into a direct sum of the form: IndGB λ = ( IndGP StM ⊗χ0 ) ⊕ ( IndGP 1M ⊗χ0 ), where P is a parabolic subgroup of G with Levi subgroup M of semi-simple rank 1, 1M is the trivial representation of M, StM is the Steinberg representation of M and χ0 is a certain character of M. We construct examples of this phenomenon for all simply-connected simple groups of rank at least 2.

KW - Intertwining operators

KW - Lie groups

KW - P-adic groups

KW - Principle series

KW - Representation theory

UR - http://www.scopus.com/inward/record.url?scp=85091381814&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85091381814

SN - 0949-5932

VL - 30

SP - 939

EP - 964

JO - Journal of Lie Theory

JF - Journal of Lie Theory

IS - 4

ER -

Singularities of intertwining operators and decompositions of principal series representations

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this