The fixed point subvarieties of unipotent transformations on the flag varieties

Naohisa SHIMOMURA

doi:10.2969/jmsj/03730537

Naohisa SHIMOMURA

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JOURNAL FREE ACCESS

1985 Volume 37 Issue 3 Pages 537-556

DOI https://doi.org/10.2969/jmsj/03730537

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Published: 1985 Received: June 22, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) C. De Concini, D. Eisenbud and C. Procesi, Hodge algebras, Asterisque 91, Société Mathématique de France, 1982.
2) M. Hochster, Grassmannians and their Schubert subvarieties are arithmetically Cohen-Macaulay, J. Algebra, 25 (1973), 40-57.
3) R. Hotta and N. Shimomura, The fixed point subvarieties of unipotent transformations on generalized flag varieties and the Green functions, Math. Ann., 241 (1979), 193-208.
4) H. Kraft and C. Procesi, Closures of conjugacy classes of matrices are normal, Invent. Math., 53 (1979), 227-247.
5) H. Kraft and C. Procesi, Minimal singularities in GL_n, Invent. Math., 62 (1981), 503-515.
6) D. Laksov, The arithmetic Cohen-Macaulay character of Schubert schemes, Acta Math., 129 (1972), 1-9.
7) G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. Math., 42 (1981), 167-178.
8) I. G. Macdonald, Symmetric functions and Hall polynomials, Clarendon Press, Oxford, 1979.
9) H. Matsumura, Commutative Algebra, Benjamin, New York, 1970.
10) C. Musili, Postulation formula for Schubert varieties, J. Indian Math. Soc., 36 (1972), 143-171.
11) C. Musili, Some properties of Schubert varieties, J. Indian Math. Soc., 38 (1974), 131-145.
12) N. Shimomura, A theorem on the fixed point set of a unipotent transformation on the flag manifold, J. Math. Soc. Japan, 32 (1980), 55-64.
13) N. Spaltenstein, Classes unipotentes et sous-groupes de Borel, Lecture Notes in Math., 946, Springer, 1982.
14) E. B. Vinberg and V. L. Popov, On a class of quasihomogeneous affine varieties, Math. USSR Izvestija, 6 (1972), 743-758.

Right : [1] C. De Concini, D. Eisenbud and C. Procesi, Hodge algebras, Asterisque 91, Société Mathématique de France, 1982.
[2] M. Hochster, Grassmannians and their Schubert subvarieties are arithmetically Cohen-Macaulay, J. Algebra, 25 (1973), 40-57.
[3] R. Hotta and N. Shimomura, The fixed point subvarieties of unipotent transformations on generalized flag varieties and the Green functions, Math. Ann., 241 (1979), 193-208.
[4] H. Kraft and C. Procesi, Closures of conjugacy classes of matrices are normal, Invent. Math., 53 (1979), 227-247.
[5] H. Kraft and C. Procesi, Minimal singularities in GL_n, Invent. Math., 62 (1981), 503-515.
[6] D. Laksov, The arithmetic Cohen-Macaulay character of Schubert schemes, Acta Math., 129 (1972), 1-9.
[7] G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. Math., 42 (1981), 167-178.
[8] I. G. Macdonald, Symmetric functions and Hall polynomials, Clarendon Press, Oxford, 1979.
[9] H. Matsumura, Commutative Algebra, Benjamin, New York, 1970.
[10] C. Musili, Postulation formula for Schubert varieties, J. Indian Math. Soc., 36 (1972), 143-171.
[11] C. Musili, Some properties of Schubert varieties, J. Indian Math. Soc., 38 (1974), 131-145.
[12] N. Shimomura, A theorem on the fixed point set of a unipotent transformation on the flag manifold, J. Math. Soc. Japan, 32 (1980), 55-64.
[13] N. Spaltenstein, Classes unipotentes et sous-groupes de Borel, Lecture Notes in Math., 946, Springer, 1982.
[14] E. B. Vinberg and V. L. Popov, On a class of quasihomogeneous affine varieties, Math. USSR Izvestija, 6 (1972), 743-758.

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