Skip to main content
Log in

Specht polynomials and modules over the Weyl algebra

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In this paper we study the decomposition structure of a direct image of a polynomial ring under certain map.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abebaw, T., Bøgvad, R.: Decomposition of D-modules over a hyperplane arrangement in the plane. Ark. Mat. 48(2), 211–229 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Allen, E.: A conjecture of Procesi and a new basis for the decomposition of the graded left regular representation of \(S_n\). Adv Math. 1100(2), 262–292 (1993)

    Article  MATH  Google Scholar 

  3. Ariki, S., Terasoma, T., Yamada, H.: Higher Specht polynomials. Hiroshima Math. 27(1), 177–188 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bergeron, F.: Algebraic combinatorics and coinvariant spaces, CMS Treatises in Mathematics. Canadian Mathematical Society, Ottawa (2009) (A K Peters Ltd., Wellesley )

  5. Björk, J.-E.: Rings of Differential Operators. North-Holland Publishing Co., Amsterdam (1979)

    Google Scholar 

  6. Björk, J.-E.: Analytic \(D\)-modules and Applications, vol. 247. Kluwer Academic Publishers Group, Dordrecht (1993)

    Book  MATH  Google Scholar 

  7. de Cataldo, M.A.A., Migliorini, L.: The decomposition theorem, perverse sheaves and the topology of algebraic maps. Bull. Am. Math. Soc. (N.S.) 46(4), 535–633 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Coutinho, S.C.: A Primer of Algebraic \(D\)-Modules, vol. 33. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  9. Fulton, W., Harris, J.: Representation Theory. A First Course, Graduate Texts in Mathematics. Readings in Mathematics, vol. 129. Springer, New York (1991)

    Google Scholar 

  10. Garsia, A., Procesi, C.: On certain graded \(S_n\)-modules and the \(q\)-Kostka polynomials. Adv. Math. 94(1), 82–138 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gille, P., Szamuely, T.: Central Simple Algebras and Galois Cohomology, vol. 101. Cambridge Studies in Advanced Mathematics, Cambridge (2006)

    Book  MATH  Google Scholar 

  12. Hartshorne, R.: Residues and Duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. With an appendix by P. Deligne. Lecture Notes in Mathematics, No. 20. Springer, Berlin, New York (1966)

  13. Hotta, R., Takeuchi, K., Tanisaki, T.: D-Modules, Perverse Sheaves, and Representation Theory. Progress in Mathematics, 236. Birkhuser Boston, Inc., Boston (2008)

  14. Peel, M.H.: Specht modules and symmetric groups. J. Algebra 36(1), 88–97 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sagan, B.E.: The Symmetric Group. Representations, Combinatorial Algorithms, and Symmetric Functions, 2nd edn. Graduate Texts in Mathematics, 203. Springer, New York (2001)

  16. Serre, J.-P.: Linear Representations of finite Groups, Graduate Texts in Mathematics, vol. 42. Springer, New York, Heidelberg (1977)

    Book  Google Scholar 

  17. Terasoma, T., Yamada, H.: Higher Specht polynomials for the symmetric group. Proc. Jpn. Acad. Ser. A Math. Sci. 69, 41–44 (1993)

  18. van der Put, M., Singer, M.S.: Galois Theory of Linear Differential Equations. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 328. Springer, Berlin (2003)

    Google Scholar 

Download references

Acknowledgements

This article is based on part of the author’s Ph.D. Dissertation written under the supervision of Prof. Rikard Bøgvad. I deeply thankful to R. Källstrom and Prof R. Bøgvad for instructive comments during the writing of this paper. This paper is financially supported by the International Science Program (ISP).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ibrahim Nonkané.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nonkané, I. Specht polynomials and modules over the Weyl algebra. Afr. Mat. 30, 279–290 (2019). https://doi.org/10.1007/s13370-018-0642-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-018-0642-9

Keywords

Mathematics Subject Classification

Navigation