Skip to main content
SpringerLink
Log in

Fusion Procedure for Degenerate Cyclotomic Hecke Algebras

  • Published:
Algebras and Representation Theory Aims and scope Submit manuscript

Abstract

The primitive idempotents of the degenerate cycloctomic Hecke algebras are derived by consecutive evaluations of a certain rational function. This rational function depends only on the Specht modules and the normalization factors are the weights of the Brundan-Kleshchev trace.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ariki, S., Mathas, A., Rui, H.: Cyclotomic Nazarov-Wenzl algebras. Nagoya Math. J. 182, 47–134 (2006)

    MATH  MathSciNet  Google Scholar 

  2. Brundan, J.: Centers of degenerate cyclotomic Hecke algebras and parabolic category \(\mathcal O\). Represent. Theory 12, 236–259 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Brundan, J., Kleshchev, A.: Schur-Weyl duality for higher levels. Sel. Math. (New Series) 14, 1–57 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Brundan, J., Kleshchev, A.: Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras. Invent. Math 178, 451–484 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cherednik, I.V.: Special bases of irreducible representations of a degenerate affine Hecke algebra. Func. Anal. Appl. 20, 76–78 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chlouveraki, M., d’Andecy, L.P.: Representation theory of the Yokonuma-Hecke algebra. arXiv:1302.6225 (2013)

  7. d’Andecy, L.P.: Fusion procedure for the Yang-Baxter equation and Schur-Weyl duality. arXiv:1307.6808 (2013)

  8. Grime, J.: The hook fusion procedure for Hecke algebras. J. Algebra 39, 744–759 (2007)

    Article  MathSciNet  Google Scholar 

  9. Isaev, A.P., Kirillov, A.N.: Bethe subalgebras in Hecke algebra and Gaudin models. arXiv:1302.6495 (2013)

  10. Isaev, A.P., Molev, A.I.: Fusion procedure for the Brauer algebra. Algebra i Analiz 22, 142–154 (2010)

    MathSciNet  Google Scholar 

  11. Os’kin, A.F.: On the idempotents of Hecke algebras. Lett. Math. Phys. 85, 79–90 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Isaev, A.P., Molev, A.I., Ogievetsky, O.: A new fusion procedure for the Brauer algebra and evaluation homomorphisms. Intel. Math. Res. Not. 11, 2571–2606 (2012)

    MathSciNet  Google Scholar 

  13. Isaev, A.P., Molev, A.I., Ogievetsky, O.: Idempotents for Birman-Murakami-Wenzl algebras and reflection equation. arXiv:1111.2502 (2011)

  14. Jucys, A.: On Young operators of the symmetric group. Liet. Fiz. Rink 6, 163–180 (1966)

    MathSciNet  Google Scholar 

  15. Kleshchev, A.: Linear and Projective Representations of Symmetric Groups. Cambridge University Press, Cambridge (2005)

    Book  MATH  Google Scholar 

  16. Kulish, P., Reshetikhin, N., Sklyanin, E.: Yang-Baxter equation and representation theory I. Lett. Math. Phys. 5, 393–403 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  17. Mathas, A.: Seminormal forms and Gram determinats for cellular algebras (With an appendix by M. Soriano). J. Reine Angew. Math. 619, 141–173 (2008)

    MATH  MathSciNet  Google Scholar 

  18. Molev, A.I.: On the fusion procedure for the symmetric group. Rep. Math. Phys. 61, 181–188 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Nazarov, M.: Yangians and Capelli identities. In: Olshanski, G.I. (ed.) Kirillov’s Seminar on Representation Theory, Amer. Math. Soc. Transl. vol. 181, pp. 139–163. American Mathematical Society, Providence (1998)

    Google Scholar 

  20. Nazarov, M.: Mixed hook-length formula for degenerate affine Hecke algebras. Lect. Notes Math. 1815, 223–236 (2003)

    Article  Google Scholar 

  21. Nazarov, M.: A mixed hook-length formula for affine Hecke algebras. European. J. Combin. 25, 1345–1376 (2004)

    Article  MATH  Google Scholar 

  22. Nazarov, M., Tarasov, V.: On irreducibility of tensor products of Yangian modules associated with skew Young diagrams. Duke Math. J. 112, 343–378 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  23. Ogievetsky, O.V., d’Andecy, L.P.: Fusion procedure for Coxeter groups of type B and complex reflection groups G(m,1,n). arXiv:1111.6293 (2011)

  24. Ogievetsky, O.V., d’Andecy, L.P.: Fusion procedure for cyclotomic Hecke algebras. arXiv:1301.4237 (2013)

  25. Shephard, G.C., Toda, J.A.: Finite unitary reflection groups. Canad. J. Math. 6, 273–304 (1954)

    Google Scholar 

  26. Zhao, D.K.: Schur elements for degenerate cyclotomic Hecke algebras. Israel J. Math. (accepted)

  27. Zhao, D.K.: The symbolic and cancellation-free formulae for Schur elements. Monatsh. Math. 173, 441–453 (2014)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Applied Mathematics, Beijing Normal University at Zhuhai, Zhuhai, 519087, China

    Deke Zhao

  2. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, China

    Yanbo Li

Authors
  1. Deke Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanbo Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Deke Zhao.

Additional information

Presented By Peter Littelmann.

Zhao is supported by the National Natural Science Foundation of China (Grant No. 11101037). Li is supported by Fundamental Research Funds for the Central Universities (N130423011) and the Natural Science Foundation of Hebei Province, China (A2013501055).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, D., Li, Y. Fusion Procedure for Degenerate Cyclotomic Hecke Algebras. Algebr Represent Theor 18, 449–461 (2015). https://doi.org/10.1007/s10468-014-9503-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10468-014-9503-x

Keywords

Mathematics Subject Classifications(2010)

Search

Navigation