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Nolan Russell Wallach is a mathematician known for the works in the representation theory of reductive algebraic groups. He is the author of the 2-volume treatise Real Reductive Groups.^[1]

Wallach did his undergraduate studies at the University of Maryland, graduating in 1962.^[2] He earned his Ph.D. from Washington University in St. Louis in 1966, under the supervision of Jun-Ichi Hano.^[2]^[3] He is a professor emeritus of mathematics at the University of California, San Diego, a fellow of the American Academy of Arts and Sciences, and a fellow of the American Mathematical Society.^[2]^[4] His doctoral students include AMS Fellow Alvany Rocha.^[3]

Selected publications

Articles

with M. do Carmo: Minimal immersions of spheres into spheres, Annals of Mathematics, vol. 93, 1971, pp. 43-62. JSTOR 1970752
Compact homogeneous Riemannian manifolds with strictly positive curvature, Annals of Mathematics, vol. 96, 1972, pp. 277-295. doi:10.2307/1970789
with D. DeGeorge: Limit formulas for multiplicities in L²(Γ \G), Annals of Mathematics, vol. 107, 1978, pp. 133-150. doi:10.2307/1971140
with Roe Goodman: Classical and quantum mechanical systems of Toda lattice type, 3 Parts, Comm. Math. Phys., Part I, vol. 83, 1982, pp. 355-386, MR0649809; Part II, vol. 94, 1984, pp. 177-217, MR0761793; Part III, vol. 105, 1986, pp. 473-509, MR0848652
with A. Rocha-Caridi: Characters of irreducible representations of the Lie algebra of vector fields on the circle, Invent. Math., vol. 72, 1983, pp. 57-75 doi:10.1007/BF01389129
with A. Rocha-Caridi: Highest weight modules over graded Lie algebras: resolutions, filtrations and character formulas, Transactions of the AMS, vol. 277, 1983, pp. 133-162 MR690045
with T. Enright, R. Howe: A classification of unitary highest weight modules, in: Representation theory of reductive groups (Park City, Utah 1982), Progress in Mathematics 40, Birkhäuser 1983, pp. 97-143 doi:10.1007/978-1-4684-6730-7_7
with A. Rocha-Caridi: Characters of irreducible representations of the Virasoro-Algebra, Mathematische Zeitschrift, vol. 185, 1984, pp. 1-21
Quantum computing and entanglement for mathematicians, in: Representation theory and complex analysis, pp. 345–376, Lecture Notes in Math. No. 1931, Springer 2008 doi:10.1007/978-3-540-76892-0_6

Books

Harmonic analysis on homogeneous spaces, New York: Marcel Dekker 1973
Symplectic geometry and Fourier analysis, Brookline: Math. Science Press 1977^[5]
Real Reductive Groups, 2 vols., Academic Press 1988, 1992
with Roe Goodman: Representations and invariants of the classical groups, Cambridge University Press 1998; 1st pbk edition, 1999; reprint with corrections, 2003
with Armand Borel: Continuous cohomology, discrete subgroups and representations of reductive groups, Annals of Mathematical Studies 94, 1980, 2nd edition, American Mathematical Society 2013
with Roe Goodman: Symmetry, representations, and invariants, Graduate Texts in Mathematics, Springer 2009

References

^ Collingwood, David H. (1990), "Review: Nolan R. Wallach, Real reductive groups. I", Bulletin of the American Mathematical Society (N.S.), 22 (1): 183–198.
^ ^a ^b ^c UCSD Mathematics Profile: Nolan Wallach, retrieved 2013-09-01.
^ ^a ^b Nolan Wallach at the Mathematics Genealogy Project
^ List of Fellows of the American Mathematical Society, retrieved 2013-09-01.
^ Marsden, Jerrold E.; Weinstein, Alan (1979). "Review of Geometric asymptotics by Victor Guillemin and Shlomo Sternberg and Symplectic geometry and Fourier analysis by Nolan R. Wallach" (PDF). Bull. Amer. Math. Soc. (N.S.). 1 (3): 545–553.

External links

Personal website

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[1] Collingwood, David H. (1990), "Review: Nolan R. Wallach, Real reductive groups. I", Bulletin of the American Mathematical Society (N.S.), 22 (1): 183–198.

[profile-2] UCSD Mathematics Profile: Nolan Wallach, retrieved 2013-09-01.

[mg-3] Nolan Wallach at the Mathematics Genealogy Project

[4] List of Fellows of the American Mathematical Society, retrieved 2013-09-01.

[5] Marsden, Jerrold E.; Weinstein, Alan (1979). "Review of Geometric asymptotics by Victor Guillemin and Shlomo Sternberg and Symplectic geometry and Fourier analysis by Nolan R. Wallach" (PDF). Bull. Amer. Math. Soc. (N.S.). 1 (3): 545–553.

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 ==Selected publications==
+===Articles===
-*with [[Manfredo do Carmo|M. do Carmo]]: Minimal immersions of  spheres into spheres, Annals of Mathematics, vol. 93, 1971, pp. 43-62.
-*Compact homogeneous Riemannian manifolds with strictly positive curvature, Annals of Mathematics, vol. 96, 1972, pp. 277-295.
+*with [[Manfredo do Carmo|M. do Carmo]]: Minimal immersions of  spheres into spheres, Annals of Mathematics, vol. 93, 1971, pp. 43-62. {{jstor|1970752}}
+*Compact homogeneous Riemannian manifolds with strictly positive curvature, Annals of Mathematics, vol. 96, 1972, pp. 277-295. {{doi|10.2307/1970789}}
+*with D. DeGeorge:  Limit formulas for multiplicities in L<sup>2</sup>(Γ{{space}}\G), Annals of Mathematics, vol. 107, 1978, pp. 133-150. {{doi|10.2307/1971140}}
+*with Roe Goodman: Classical and quantum mechanical systems of Toda lattice type, 3 Parts, Comm. Math. Phys., Part I, vol. 83, 1982, pp. 355-386, {{MR|0649809}}; Part II, vol. 94, 1984, pp. 177-217, {{MR|0761793}}; Part III, vol. 105, 1986, pp. 473-509, {{MR|0848652}}
+*with A. Rocha-Caridi: Characters of irreducible representations of the Lie algebra of vector fields on the circle, Invent. Math., vol. 72, 1983, pp. 57-75 {{doi|10.1007/BF01389129}}
+*with A. Rocha-Caridi: Highest weight modules over graded Lie algebras: resolutions, filtrations and character formulas, Transactions of the AMS, vol. 277, 1983, pp. 133-162 {{MR|690045}}
+*with T. Enright, [[Roger Evans Howe|R. Howe]]: A classification of unitary highest weight modules, in: Representation theory of reductive groups (Park City, Utah 1982), Progress in Mathematics 40, Birkhäuser 1983, pp. 97-143 {{doi|10.1007/978-1-4684-6730-7_7}}
+*with A. Rocha-Caridi: [http://eudml.org/doc/173382 Characters of irreducible representations of the Virasoro-Algebra], Mathematische Zeitschrift, vol. 185, 1984, pp. 1-21
+*Quantum computing and entanglement for mathematicians, in: Representation theory and complex analysis, pp. 345–376, Lecture Notes in Math. No. 1931, Springer 2008 {{doi|10.1007/978-3-540-76892-0_6}}
+===Books===
 *Harmonic analysis on homogeneous spaces, New York: Marcel Dekker 1973
-*with D. DeGeorge:  Limit formulas for multiplicities in L2( G\G), Annals of Mathematics, vol. 107, 1978, pp. 133-150.
-*with [[Armand Borel]]: Continuous cohomology, discrete subgroups and representations of reductive groups, Annals of Mathematical Studies 94, 1980, American Mathematical Society 2000
-*with Roe Goodman: Representations and invariants of the classical groups, Cambridge University Press 1998
 *Symplectic geometry and Fourier analysis, Brookline: Math. Science Press 1977<ref>{{cite journal|author=Marsden, Jerrold E.|authorlink=Jerrold E. Marsden|author2=Weinstein, Alan|authorlink2=Alan Weinstein|journal=Bull. Amer. Math. Soc. (N.S.)|volume=1|number=3|pages=545–553|year=1979|title=Review of ''Geometric asymptotics'' by Victor Guillemin and Shlomo Sternberg and ''Symplectic geometry and Fourier analysis'' by Nolan R. Wallach|url=http://www.ams.org/journals/bull/1979-01-03/S0273-0979-1979-14617-2/S0273-0979-1979-14617-2.pdf}}</ref>
-*with A. Rocha-Caridi: Characters of irreducible representations of the Lie algebra of vector fields on the circle, Invent. Math., vol. 72, 1983, pp. 57-75
-*with A. Rocha-Caridi: Characters of irreducible representations of the Virasoro-Algebra, Mathematische Zeitschrift, vol. 185, 1984, pp. 1-21
-*with A. Rocha-Caridi: Highest weight modules over graded Lie algebras: resolutions, filtrations and character formulas, Transactions of the AMS, vol. 277, 1983, pp. 133-162
-*with T. Enright, [[Roger Evans Howe|R. Howe]]: A classification of unitary highest weight modules, in: Representation theory of reductive groups (Park City, Utah 1982), Progress in Mathematics 40, Birkhäuser 1983, pp. 97-143
 *Real Reductive Groups, 2 vols., Academic Press 1988, 1992
+*with Roe Goodman: Representations and invariants of the classical groups, Cambridge University Press 1998; 1st pbk edition, 1999; [http://books.google.com/books?id=KBFoV2jpnPUC reprint with corrections], 2003
-*with Roe Goodman: Classical and quantum mechanical systems of Toda lattice type, 3 Teile, Comm. Math. Phys., vol. 83, 1982, pp. 355-386, vol. 94, 1984, pp. 177-217, vol. 105, 1986, pp. 473-509
+*with [[Armand Borel]]: Continuous cohomology, discrete subgroups and representations of reductive groups, Annals of Mathematical Studies 94, 1980, [http://books.google.com/books?id=bYYCAQAAQBAJ 2nd edition], American Mathematical Society 2013
-*with Roe Goodman: Symmetry, representations, and invariants, Graduate Texts in Mathematics, Springer 2009
+*with Roe Goodman: [http://books.google.com/books?id=tbSX5VPE4PIC Symmetry, representations, and invariants], Graduate Texts in Mathematics, Springer 2009
-*Quantum computing and entanglement for mathematicians, in: Representation theory and complex analysis, pp. 345–376, Lecture Notes in Math. No. 1931, Springer 2008
 == References ==