Selected
Mathematical Works
Alfred
G. Noël
Refereed Papers
· Classification of Admissible Nilpotent
Orbits in Simple Exceptional Lie Algebras of Type E6(6) and E6(-26) American Mathematical Society Journal of
Representation Theory, Volume 5 (494-502) 2001
·
Computing
maximal tori using LiE and Mathematica.
Lectures Notes in Computer Science,
Springer-Verlag. Vol 2657 (728-736) 2003.
·
Computing
theta-stable parabolic subalgebras using LiE. Lectures Notes in Computer
Science, Springer-Verlag
Volume 3039 (335-342) 2004.
· A LiE subroutine for computing prehomogeneous spaces
associated with nilpotent Complex Orbits Co-author Steven Glenn Jackson Lecture
Notes in Computer Science, Springer-Verlag Vol 3516, (611—618),
200
· A LiE subroutine for computing prehomogeneous spaces
associated to real nilpotent orbits Co-author Steven Glenn Jackson Lecture Notes in Computer Science, Springer-Verlag Vol 3482, (512—521), 2005
· Prehomogeneous spaces associated with
complex nilpotent orbits Co-author Steven Glenn Jackson Journal of Algebra
Volume 289, Issue 2, (515-557) 2005.
· Prehomogeneous spaces associated to
nilpotent orbits in simple real Lie algebras E6(6) and E6(-26) Co-author
Steven Glenn Jackson. Experimental Mathematics Volume 15, Isuue 4, (455-469)
2006.
· Some remarks on Richardson orbits in
complex symmetric spaces American
Mathematical Society Mathematics of Computation. Volume 75 (395-417), 2006.
- Prehomogeneous spaces associated
with real nilpotent orbits, with Steven Glenn Jackson. Journal of Algebra Volume 305, Issue 1, (194-269) 2006.
- Polarizable theta-stable parabolic
subalgebras and $K_C$-saturation in the non-compact real forms of $G_2$
and $F_4$, with Steven Glenn
Jackson. Lecture Notes in Computer Science, Springer-Verlag Vol 3992,
(422—429), 2006.
- A general computational scheme for
testing admissibility of nilpotent orbits of real Lie groups of inner type. Lecture Notes in Computer Science, Springer-Verlag
Vol 4151, (1—11), 2006.
- Maximal
Tori of Reductive Centralizers of Nilpotents in Complex Symmetric Space American Mathematical Society Contemporary
Mathematics, Volume 467 (103 – 139) 2008.
- The
Atlas of Lie groups and representations: scope and successes American Mathematical Society Contemporary
Mathematics, Volume 467 (85 – 101) 2008.
- A new approach for computing
generators for U(g)^K with Steven
Glenn Jackson (Submitted)
2008.
- Nilpotent Orbits attached to
Coxeter Cells with Steven
Glenn Jackson (Submitted) 2008.
Memoirs and Books
- Ph.
D. Thesis, Northeastern University, March 1997.
- Council for African American
Researchers in the Mathematical Sciences: Volume III. Fifth Conference for
African American Researchers in the Mathematical Sciences, June 22-25,
1999, University of Michigan, Ann Arbor, Michigan. Alfred G. Noël, Earl Barnes, Sonya A. F. Stephens
Editors. American Mathematical Society Contemporary Mathematics, Volume
275. (2001)
- Council for African American
Researchers in the Mathematical Sciences: Volume V. Thirteenth Conference
for African American Researchers in the Mathematical Sciences, June 19-22,
2007, Northeastern University and the University of Massachusetts Boston. Alfred G. Noël, Donald R. King, Gaston M.
N’Guérékata, Edray H. Goins
Editors. American Mathematical Society Contemporary Mathematics,
Volume 467. (2008)
Problems
·
A
canonical basis for maximal tori of the reduc tive centralizer of a nilpotent
element Proceedings of the NATO Advanced Study
Institute Computational Noncommutative Algebra and Applications
July 6--19, 2003 Il Ciocco Resort Hotel, Italy. Edited by Jim Byrnes, Nato Science Series II. Mathematics, Physics and
Chemistry – Vol. 136.
Expository Papers and Selected Talks
- TITS SYSTEMS,
PARABOLIC SUBGROUPS, PARABOLIC SUBALGEBRAS, Northeastern University,
June 1996. This paper was written as part of the requirements for a
course, Topics in algebraic geometry, taught by Prof. V. Lakshmibai in the
Spring 1996 quarter. Click here to
download the postscript version
- NOTICED
NILPOTENT ORBITS OF REAL LIE ALGEBRAS. This is the content of a
poster presentation at the Third CAARMS meeting in Baltimore Maryland in
June 1997. Click here to download the
postscript version.
- CENTRALIZERS
OF NILPOTENTS AND THE BALA-CARTER CLASSIFICATION. This is the
content of a talk given at the GASC seminar at Northeastern University on
June 7, 1999. Click here to download the
postscript version.
- COMPONENT GROUPS OF CENTRALIZERS OF NILPOTENTS IN
SYMMETRIC SPACES.
This file contains
a talk that was given at CAARMS5, University of Michigan, in June 99. The
general theory is studied using the group SL(n,R) as an example. This is
for an audience of non-specialists. There is no Lie structure theory.
Everything is done in thecontext of Linear Algebra. Click here to download the postscript version.
- ON THE
ADMISSIBILITY OF NILPOTENT ORBITS OF SIMPLE EXCEPTIONAL REAL LIE GROUPS OF
INNER TYPE. This is
the content of a talk given at an AMS Sectional Meeting held at University
of South Carolina Columbia on March 16-18, 2001, Special Session on
Algebraic Structures Associated with Lie Theory, III.
- Quantization in Physics
and Mathematics, Science Colloquium Hour The University of
Massachusetts Boston April 9, 2004
- Richardson
Orbits for Real Semisimple Lie Groups Conference on Nilpotent Orbits and Representation
Theory, 2004 Fuji-Zakura So, Japan
September 5-10 2004
- Prehomogeneous
Spaces Associated with Nilpotent Orbits of Complex Lie Groups
AMS Special Session on Representations of Lie Algebras AMS Joint Mathematical Meeting
January 5- 8, 2005 Atlanta Georgia.
- A LiE
subroutine for computing prehomogeneous spaces associated to real nilpotent orbits International Conference on
Computational Science and its Applications (ICCSA 2005) May 9 - 12, 2005
Suntec, Singapore, Singapore.
- The Atlas
of Lie groups and representations: scope and successes CAARMS 13 June
19-22, 2007 Boston MA
- The
Uncontroversial Mathematics Behind Garrett Lisi’s Controversial ``Theory
of Everything’’ (In Memory of My Grandmother Vilicia Auguste: 1914 –
2008). Société Scientifique Haïtienne (HSS), University of
Massachusetts Boston, July 26, 2008.
Preprints, Tables and Work in Progress
- Associating elliptic Pseudo-Levi
subalgebras to nilpotent conjuagcy classes in the classical simple real
Lie algebras. (Unfinished
manuscript)
· Maximal Tori of
Reductive Centralizers of Nilpotents . (tables).
· Tables of prehomogeneous spaces
associated with exceptional Lie algebras
http://www.math.umb.edu/~anoel/publications/tables
Funded Proposals
- AY 1998-99 Faculty Internal Grants
Program. This proposal was written in
March 1999 for a UmassBoston competition . My goal was to acquire internal
funds for equipment and travels.It contains a research proposal which may
give some insight on future work and proposals.
- Martin Luther King Professorship at MIT. This
proposal was at the basis of the MLK professorship which was awarded
during the 2000-2001 academic year by the Mathematics department of the
Massachusetts Institute of Technology .
- National Science Foundation Research
Opportunity Award. This proposal was funded for a year (3/2002 -
3/2003) by the NSF for work to be done at the Massachusetts Institute of
Technology with David Vogan.