94
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

On the Classification of Orbits of Symmetric Subgroups Acting on Flag Varieties of SL(2, k)

&
Pages 1334-1352 | Received 19 Feb 2007, Published online: 28 Mar 2009

REFERENCES

  • Abeasis , S. ( 1988 ). On a remarkable class of subvarieties of a symmetric variety . Adv. Math. 71 ( 1 ): 113 – 129 .
  • Bei˘linson , A. , Bernstein , J. ( 1981 ). Localisation de g-modules . C. R. Acad. Sci. Paris Sér. I Math. 292 ( 1 ): 15 – 18 .
  • Borel , A. (1991). Linear Algebraic Groups , 2nd. Volume 126 of Graduate Texts in Mathematics. ed. New York : Springer-Verlag.
  • Brion , M. , Helminck , A. G. ( 2000 ). On orbit closures of symmetric subgroups in flag varieties . Canad. J. Math. 52 ( 2 ): 265 – 292 .
  • Brylinski , J.-L. , Delorme , P. ( 1992 ). Vecteurs distributions H-invariants pour les séries principales généralisées d'espaces symétriques réductifs et prolongement méromorphe d'intégrales d' Eisenstein . Invent. Math. 109 ( 3 ): 619 – 664 .
  • De Concini , C. , Procesi , C. ( 1983 ). Complete symmetric varieties. In: Invariant Theory (Montecatini, 1982) . Volume 996 of Lecture Notes in Math . Berlin : Springer , pp. 1 – 44 .
  • De Concini , C. , Procesi , C. ( 1985 ). Complete symmetric varieties. II. Intersection theory . In: Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983) . Volume 6 of Adv. Stud. Pure Math . Amsterdam : North-Holland , pp. 481 – 513 .
  • Delorme , P. ( 1998 ). Formule de plancherel pour les espaces symétriques réductifs . Ann. Math. (2) 147 ( 2 ): 417 – 452 .
  • Flensted-Jensen , M. ( 1980 ). Discrete series for semisimple symmetric spaces . Ann. Math. (2) 111 ( 2 ): 253 – 311 .
  • Grojnowski , I. ( 1992 ). Character Sheaves on Symmetric Spaces. PhD thesis , Massachusetts Institute of Technology .
  • Harish-Chandra ( 1984 ). Collected Papers . Vol. I–IV . Varadarajan , V. S. , ed. New York : Springer-Verlag , pp. 1970 – 1983 .
  • Helminck , A. G. ( 2004 ). Combinatorics related to orbit closures of symmetric subgroups in flag varieties . In: Invariant Theory in all Characteristics . Volume 35 of CRM Proc. Lecture Notes . Providence , RI : Amer. Math. Soc. , pp. 71 – 90 .
  • Helminck , A. G. , Helminck , G. F. H k -fixed distribution vectors for representations related to 𝔭-adic symmetric varieties . In preparation .
  • Helminck , A. G. , Wang , S. P. ( 1993 ). On rationality properties of involutions of reductive groups . Adv. Math. 99 ( 1 ): 26 – 96 .
  • Helminck , A. G. , Wu , L. ( 2002 ). Classification of involutions of SL(2, k) . Comm. Algebra 30 ( 1 ): 193 – 203 .
  • Hirzebruch , F. , Slodowy , P. ( 1990 ). Elliptic genera, involutions, and homogeneous spin manifolds . Geom. Dedicata 35 ( 1–3 ): 309 – 343 .
  • Humphreys , J. E. ( 1975 ). Linear Algebraic Groups . Graduate Texts in Mathematics, No. 21 . New York : Springer-Verlag .
  • Lusztig , G. ( 1990 ). Symmetric spaces over a finite field . In: The Grothendieck Festschrift . Vol. III . Volume 88 of Progr. Math . Boston , MA : Birkhäuser Boston Inc. , pp. 57 – 81 .
  • Lusztig , G. , Vogan , D. A. , Jr. ( 1983 ). Singularities of closures of K-orbits on flag manifolds . Invent. Math. 71 ( 2 ): 365 – 379 .
  • Matsuki , T. ( 1979 ). The orbits of affine symmetric spaces under the action of minimal parabolic subgroups . J. Math. Soc. Japan 31 ( 2 ): 331 – 357 .
  • Ōshima , T. , Sekiguchi , J. ( 1980 ). Eigenspaces of invariant differential operators on an affine symmetric space . Invent. Math. 57 ( 1 ): 1 – 81 .
  • Ōshima , T. , Matsuki , T. ( 1984 ). A description of discrete series for semisimple symmetric spaces . In: Group Representations and Systems of Differential Equations (Tokyo, 1982) . Volume 4 of Adv. Stud. Pure Math . Amsterdam : North-Holland , pp. 331 – 390 .
  • Rossmann , W. ( 1979 ). The structure of semisimple symmetric spaces . Canad. J. Math. 31 ( 1 ): 157 – 180 .
  • Serre , J.-P. ( 1973 ). A Course in Arithmetic . Translated from the French, Graduate Texts in Mathematics, No. 7 . New York : Springer-Verlag .
  • Springer , T. A. ( 1985 ). Some results on algebraic groups with involutions . In: Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983) . Volume 6 of Adv. Stud. Pure Math . Amsterdam : North-Holland , pp. 525 – 543 .
  • Springer , T. A. (1998). Linear Algebraic Groups , 2nd. Volume 9 of Progress in Mathematics. ed. Boston , MA : Birkhäuser Boston Inc.
  • Steinberg , R. ( 1968 ). Endomorphisms of Linear Algebraic Groups . Memoirs of the American Mathematical Society, No. 80 . Providence , R.I. : American Mathematical Society .
  • Tong , Y. L. , Wang , S. P. ( 1989 ). Geometric realization of discrete series for semisimple symmetric spaces . Invent. Math. 96 ( 2 ): 425 – 458 .
  • van den Ban , E. P. , Schlichtkrull , H. ( 1997 ). The most continuous part of the plancherel decomposition for a reductive symmetric space . Ann. Math. (2) 145 ( 2 ): 267 – 364 .
  • Vogan , D. A. , Jr. ( 1982 ). Irreducible characters of semisimple Lie groups. IV. Character-multiplicity duality . Duke Math. J. 49 ( 4 ): 943 – 1073 .
  • Vogan , D. A. ( 1983 ). Irreducible characters of semisimple Lie groups. III. Proof of Kazhdan-Lusztig conjecture in the integral case . Invent. Math. 71 ( 2 ): 381 – 417 .
  • Winterhof , A. ( 1998 ). On the distribution of powers in finite fields . Finite Fields Appl. 4 ( 1 ): 43 – 54 .
  • Communicated by K. C. Misra.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.