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Austrian-American mathematician
Friederich Ignaz Mautner (14 May 1921–2002)
[1] was an Austrian-American mathematician, known for his research on the
representation theory of groups,
functional analysis , and
differential geometry . He is known for
Mautner's Lemma and Mautner's Phenomenon in the representation theory of
Lie groups .
[2]
Life and career
Following the
Anschluss in 1938, Mautner, a Jew, emigrated from Austria to the UK where he became one of the thousands or refugees who were interred by the British and shipped off to
Hay Camp 7 in Australia. While there he was fortunate in that he got to study mathematics under
Felix Behrend . When he got back to the UK, he garnered a BSc at
Durham University and then went to Ireland in 1944 where he got an assistantship with Paul Ewald at
Queens University Belfast (QUB).
[3] He then became a scholar at the
Dublin Institute for Advanced Studies in 1944–1946.
[4]
He then moved to the USA, where he was a visiting scholar
[5] at the
Institute for Advanced Study (IAS) in Princeton (1946-47).
[6]
He then attended
Princeton University and got a Ph.D. in 1948 with the thesis Unitary Representations of Infinite Groups .
[7]
He was a
Guggenheim Fellow at
Johns Hopkins University in the academic year 1954-55.
[8]
Working in the fields of
ergodic theory of
geodesic flows , he published a paper in 1957 that established the lemma and the phenomenon that bear his name.
[9]
He published a ground-breaking paper in 1958 that established him as a pioneer in the
representation theory of reducible
p-adic groups .
[10]
The Mautner Group, a special five-dimensional
Lie group , is named after him.
[11]
Frederich had one daughter, Jean Mautner.
Selected works
Mautner, F. I. (February 1948).
"The Completeness of the Irreducible Unitary Representations of a Locally Compact Group" . Proc Natl Acad Sci U S A . 34 (2): 52–54.
doi :
10.1073/pnas.34.2.52 .
PMC
1062914 .
PMID
16588786 .
Mautner, F. I. (1950). "Unitary representations of locally compact groups I". Annals of Mathematics . Second Series. 51 (1): 1–24.
doi :
10.2307/1969494 .
JSTOR
1969494 .
Mautner, F. I. (1950). "Unitary representations of locally compact groups II". Annals of Mathematics . Second Series. 52 (3): 528–556.
doi :
10.2307/1969431 .
JSTOR
1969431 .
Mautner, F. I. (1950).
"Infinite-dimensional irreducible representations of certain groups" . Proc. Amer. Math. Soc . 1 (5): 582–584.
doi :
10.1090/s0002-9939-1950-0039728-2 .
MR
0039728 .
Mautner, F. I. (1951).
"The regular representation of a restricted product of finite groups" . Trans. Amer. Math. Soc . 70 (3): 531–548.
doi :
10.1090/s0002-9947-1951-0041855-6 .
MR
0041855 .
Mautner, F. I. (1951).
"On the decomposition of unitary representations of Lie groups" . Proc. Amer. Math. Soc . 2 (3): 490–496.
doi :
10.1090/s0002-9939-1951-0041856-3 .
MR
0041856 .
Mautner, F. I. (July 1951).
"A Generalization of the Frobenius Reciprocity Theorem" . Proc Natl Acad Sci U S A . 37 (7): 431–435.
doi :
10.1073/pnas.37.7.431 .
PMC
1063394 .
PMID
16578378 .
Mautner, F. I. (August 1951).
"Fourier Analysis and Symmetric Spaces" . Proc Natl Acad Sci U S A . 37 (8): 529–533.
doi :
10.1073/pnas.37.8.529 .
PMC
1063414 .
PMID
16578390 .
Mautner, F. I. (January 1953).
"On Eigenfunction Expansions" . Proc Natl Acad Sci U S A . 39 (1): 49–53.
doi :
10.1073/pnas.39.1.49 .
PMC
1063724 .
PMID
16589235 .
Mautner, F. I. (January 1954).
"Geodesic Flows and Unitary Representations" . Proc Natl Acad Sci U S A . 40 (1): 33–36.
doi :
10.1073/pnas.40.1.33 .
PMC
527933 .
PMID
16589421 .
with
L. Ehrenpreis : Ehrenpreis, L.; Mautner, F. I. (15 April 1955).
"Uniformly bounded representations of groups" . Proc Natl Acad Sci U S A . 41 (4): 231–233.
doi :
10.1073/pnas.41.4.231 .
PMC
528064 .
PMID
16589653 .
Mautner, F. I. (1955).
"Note on the Fourier inversion formula on groups" . Trans. Amer. Math. Soc . 78 (2): 371–384.
doi :
10.1090/s0002-9947-1955-0067230-x .
MR
0067230 .
with L. Ehrenpreis: Ehrenpreis, L.; Mautner, F. I. (1957).
"Some properties of the Fourier transform on semi-simple Lie groups. II" . Trans. Amer. Math. Soc . 84 : 1–55.
doi :
10.1090/s0002-9947-1957-0083683-7 .
MR
0083683 .
with L. Ehrenpreis: Ehrenpreis, L.; Mautner, F. I. (1957).
"Some properties of the Fourier transform on semi-simple Lie groups. III" . Trans. Amer. Math. Soc . 90 (3): 431–484.
doi :
10.1090/s0002-9947-1959-0102755-3 .
MR
0102755 .
References
^ Biographical information from
Kühler Abschied - Wien 1938 und der Exodus der Mathematik , Ausstellung der Österreichischen Mathematischen Gesellschaft in der Universität Wien 2001
^
Moore, Calvin C. (1980).
"The Mautner phenomenon for general unitary representations" . Pacific J. Math . 86 (1): 155–169.
doi :
10.2140/pjm.1980.86.155 .
^
An Irish Sanctuary by Gisela Holfter and Horst Dickel, Walter de Gruyter GmbH, Berlin, p. 344, ISBN 978-3-11-035144-6
^
Mautner, F.I. 1944–46 Scholar, Dublin Institute for Advanced Studies
^ He would again be at the IAS in 1954-56 and in 1965-66.
^
Mautner, Friederich I., Institute for Advanced Study
^
Friederich I. Mautner at the
Mathematics Genealogy Project
^
Friederich I. Mautner; Fellow: Awarded 1954; Field of Study: Mathematics
John Simon Guggenheim Memorial Foundation
^ Mautner Geodesic flows on symmetric Riemannian spaces , Annals of Mathematics, vol. 65, 1957, pp. 416-430
^ Mautner Spherical functions over p-adic fields . I, Amer. J. Math. 80 (1958), 441–457; Part 2 appeared 6 years later in Amer. J. Math., vol. 86, 1964, S. 171-200
^
Baggett, Merrill Representations of the Mautner group and cocycles of an irrational rotation Michigan Math. J., vol. 33, 1986, 221-229