Selected Mathematical Works

Alfred G. Noël

Refereed Papers

• Progress and Process in Math Excel at Northeastern University. Co authors Maurice P. Gilmore, Thomas P. Stephens,Jr. The Center for Innovation in Urban Education Studies, Volume II, 1996 edited by J. Frazer, Northeastern University.
• Classification of Nilpotent Orbits in Symmetric Spaces. Proceedings of the American Mathematical Society DIMACS African Americans in Mathematical Sciences volume 34 (123-127) 1997. 
• Nilpotent Orbits and Theta-stable Parabolic Subalgebras. American Mathematical Society Journal of Representation Theory, Volume 2 (1-32) 1998. Click here to get postscript version
• Component Groups of Centralizers of Nilpotents in Symmetric Space. Co-author Donald R. King . Journal of Algebra Vol 232 (94-125) 2000. Click here to get postscript version
• Classification of Admissible Nilpotent Orbits in Simple Exceptional Lie Algebras of Inner Type. American Mathematical Society Journal of Representation Theory, Volume 5 (455-493) 2001.

· 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), 2005

· 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 (To appear in American Mathematical Society Contemporary Mathematics) 2008.
• The Atlas of Lie groups and representations: scope and successes (To appear in American Mathematical Society Contemporary Mathematics) 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

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.