**Publications:**

(The blue underlined publications
are available in PDF format. They can be viewed and printed with the free Adobe
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*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., Congr. Numer. (with D. J. Gagliardi). 180 (2007), 5-20.*Implementation of*Algorithms for computing characters for symmetric spaces*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.