Publications:

(The blue underlined publications are available in PDF format. They can be viewed and printed with the free Adobe Acrobat Reader. Click here to get the latest version.)

• On Generalized Cartan subspaces, (with G. Schwarz), Transformation Groups, (23 pages).To Appear.
• Equivalent forms of multi component Toda hierarchies. Journal of Geometry and Physics, 61 (2011) 847–873. (with G.F. Helminck and A.V. Opimakh).
• The relative frame bundle of a flag variety and solutions of integrable hierarchies. Theoretical and Mathematical Physics. (with G.F. Helminck and A.V. Opimakh). To Appear.
• Computing admissible sequences for twisted involutions in Weyl groups, (with R. Haas), Can. Math. Bull. (15 pages). To Appear.
• Intertwining operators related to distribution vectors for p-adic symmetric varieties. (with G.F. Helminck). To Appear.
• A data structure for the exceptional Weyl groups of type F4 and G2, (with P. Cahn, R. Haas, J. Li, and J. Schwartz),To Appear.
• Classification of involutions of SO(n; k; B), (with C. E. Dometrius and L. Wu). To Appear.
• Commuting involutions of SL(n,k), (with K. Thompson), 34 pages, to Appear.
• Algorithms for twisted involutions in Weyl groups, (with R. Haas), Algebraic Colloqium, (14 pages). To Appear.
• On orbit decompositions for Symmetric k-varieties, Progr. Math., 278, 83-127,  (2010).
• On the classification of orbits of symmetric varieties acting on flag varieties of SL(2,k), (with S. Beun), Comm. Algebra 37 (2009), no. 4, 1334-1352.
• Real double coset spaces and their invariants, (with G. Schwarz), J. Algebra 322 (2009), no. 1, 219-236.
• Algorithms for computing characters for symmetric spaces, (with D.J. Gagliardi). Acta Appl. Math. 99 (2007), no. 3, 339-365.
• Involutions of SL(n, k), (n > 2), (with C. E. Dometrius and L. Wu), Acta Appl. Math. 90 (2006), no. 1-2, 91–119.
• Implementation of Algorithms for computing characters for symmetric spaces, Congr. Numer. (with D. J. Gagliardi). 180 (2007), 5-20.
• Properties of Twisted Involutions in Signed Permutation Notation, Journal of Combinatorial Math. and Combinatorial Computing, (with R. Haas and N. Rizki), 62 (2007), 121-128.
• Implementing an algorithm for the twisted involution poset for Weyl groups, (2006), Congressus Numerantium, (with K. Brennemann and R. Haas). 182 (2007), 137-144.
• Computing the fine structure of real reductive symmetric spaces, (with J. R. Fowler), J. Symbolic Comput. 42 (2007), no. 5, 497-510.
• Involutions of SL(n, k), (n > 2), (with C. E. Dometrius and L. Wu), Acta Appl. Math. 90 (2006), no. 1-2, 91–119.
• Multiplicity one for representations corresponding to spherical distribution vectors of class &rho, (with G.F. Helminck), Acta Appl. Math., 86 (2005), no. 1-2, 21-48.
• Algorithms for computations in local symmetric spaces, (with Jennifer Fowler), Communications in Algebra, 36, 1758-1788 (2008).
• Combinatorics related to orbit closures of symmetric subgroups in flag varieties. Invariant theory in all characteristics, CRM Proc. Lecture Notes, 35, Amer. Math. Soc., (2004), 71-90.
• Smoothness of quotients associated with a pair of commuting involutions, (with Gerry Schwarz), Can. Journal Math., 56 (2004), no. 5, 945-962.
• Hilbert Flag Varieties and their Kahler structure, (with G.F. Helminck), J. Physics A., 35 (2002), no. 40, 8531-8550.
• Spherical distribution vectors, (with G.F. Helminck), Acta Appl. Math., 73 (2002), no. 1-2, 39-57.
• Orbits and invariants associated with a pair of spherical varieties, (with Gerry Schwarz), Acta Appl. Math., 73 (2002), no. 1-2, 103-113.
• Classification of involutions of SL(2, k). (with Ling Wu), Comm. in Algebra, 30 (2002), no. 1, 193--203.
• Orbits and invariants associated with commuting involutions, (with Gerry Schwarz), Duke Math. Journal, Vol. 106 (2001), No.2, 237-280.
• On orbit closures of symmetric subgroups in flag varieties, (with Michel Brion), Can. Journal Math., Vol 52 (2), (2000), pp. 265-292.
• Computing orbits of minimal parabolic k-subgroups acting on symmetric k-varieties. J. Symb. Comp. 30, (2000), 521-553.
• Multiplicities for representations related to p-adic symmetric varieties, (with G.F. Helminck), (29 pages).
• On the classification of k-involutions, Adv. in Math. 153, no. 1, (2000), 1-117.
• A Conjugacy Theorem for Symmetric Spaces (with J. Hilgert, A. Neumann and G. Olafsson), Mathematische Annalen, 313, (1999), 785-791.
• A class of parabolic k-subgroups associated with symmetric k-varieties. (with G.F. Helminck) Trans. Amer. Math. Soc. 350, (1998), 4669-4691.
• Tori Invariant under an Involutorial Automorphism II, Adv. in Math. 131, no. 1, (1997), 1-92.
• Computing B-orbits on G/H, J. Symb. Comp. Vol. 21, (1996) 169-209.
• Infinite dimensional flag manifolds in integrable systems, Acta Appl. Math. 41 (1995), 99-121. (jointly with G.F. Helminck).
• The structure of Hilbert Flag Varieties, (with G.F. Helminck). Publ. Res. Inst. Math. Sci., Kyoto Univ. 30, (1994), 401-442.
• Symmetric k-varieties, Algebraic Groups and Their Generalizations: Classical Methods (Providence, RI), vol. 56, Proc. Sympos. Pure Math. no. Part 1, Amer. Math. Soc, 1994, pp. 233-279.
• Holomorphic line bundles on Hilbert flag varieties, (with G.F. Helminck). Algebraic Groups and Their Generalizations: Quantum and Infinite-Dimensional Methods (Providence, RI), vol. 56, Proc. Sympos. Pure Math., no. Part 2, Amer. Math. Soc, 1994, pp. 349-375.
• On rationality properties of involutions of reductive groups. (with S. P. Wang). Adv. in Math. 99 (1993), 26-97.
• On groups with a Cartan involution, Proceedings of the Hyderabad conference on Algebraic Groups (Hyderabad, India), National Board for Higher Mathematics, 1992, pp. 151-192.
• Tori Invariant under an Involutorial Automorphism I, Adv. in Math. 85 (1991), 1-38.
• On the orbits of affine symmetric spaces under the action of a parabolic subgroup, Contemporary Math. 88 (1989), 435-447.
• Algebraic groups with a commuting pair of involutions and semisimple symmetric spaces, Adv. in Math. 71 (1988), 21-91.
• Trilinear alternating forms on a vector space of dimension 7. (with A.M. Cohen). Comm. in Algebra, 16 (1) (1988), 1-25.
• A classification of semisimple symmetric spaces and their restricted root system, In: ``Lie algebras and related topics'', C.B.M.S. Conf. Proc. 5, pages: 333-340, 1986.
• Classification of Real semisimple Lie algebras. In: ``The structure of real semisimple Lie groups'' (T. Koornwinder, et al. eds.), MC Syllabus 49, pages: 113-136, 1982.

Books:

• Symmetry and spaces. In honor of Gerry Schwarz. Progress in Mathematics, 278. Birkhäuser Boston, Inc., Boston, MA, 2010. ( Jointly with H. E. A. Campbell, Hanspeter Kraft and
  David Wehlau).

Publications in preparation:

• Tori Invariant under an Involutorial Automorphism III, Real groups. (61 pages), under revision.
• On maximal k-split tori invariant under an involution. (with C Buell).
• Combinatorial properties of the Richardson-Springer involution poset, (with C. Cooley, R. Haas, and N. Williams).
• Combinatorics and characterizations for involutions and twisted involutions. (with C. Baltera, K. Brenneman, A. Hatfield, R. Haas, and B. Tramel).
• Cartan subspaces for p-adic symmetric spaces.
• On the harmonic analysis of the symmetric pair (SL(2,k), D(2,k)).
• Hamiltonian cycles in Cayley graphs. (with Carla Savage)

Books in preparation:

• Integrable Systems: Algebraic and Geometric aspects of integrable Hierarchies, In preparation. (Springer GTM Series). Jointly with G.F. Helminck.
• Real Lie Groups and Semisimple Symmetric Spaces.
• Computational aspects of Symmetric Spaces.

Maple Code:

• Involution poset for twisted involutions in Weyl groups.