Skip to main content
SpringerLink
Log in

Tensor polynomial identities

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Tensor polynomial identities generalize the concept of polynomial identities on d × d matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their associated Young diagrams. Furthermore, we provide a method to evaluate arbitrary alternating tensor polynomials in d2 variables.

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. E. Aljadeff, A. Giambruno, C. Procesi and A. Regev, Rings With Polynomial Identities and Finite Dimensional Representations of Algebras, American Mathematical Society Colloquium Publications, Vol. 66, American Mathematical Society, Providene, RI, 2020.

    MATH  Google Scholar 

  2. B. Collins and P. Śniady, Integration with respect to the Haar measure on unitary, orthogonal and symplectic group, Communications in Mathematical Physics 264 (2006), 773–795.

    Article  MathSciNet  Google Scholar 

  3. E. Formanek, A conjecture of Regev about the Capelli polynomial, Journal of Algebra 109 (1987), 93–114.

    Article  MathSciNet  Google Scholar 

  4. F. Huber, Positive maps and trace polynomials from the symmetric group, Journal of Mathematical Physics 62 (2021), Article no. 022203.

  5. B. Kostant, A theorem of Frobenius, a theorem of Amitsur-Levitski and cohomologytheory, Journal of Mathematics and Mechanics 7 (1958), 237–264.

    MATH  Google Scholar 

  6. C. Procesi, Tensor polynomial or trace identities, in preparation.

  7. C. Procesi, Lie Groups, Universitext, Springer, New York, 2007.

    MATH  Google Scholar 

  8. C. Procesi, A note on the Formanek Weingarten function, Note di Matematica 41 (2021), 69–109.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Optics Department, Jagiellonian University, 30-348, Kraków, Poland

    Felix Huber

  2. Dipartimento di Matematica Guido Castelnuovo, Università degli Studi di Roma, La Sapienza Piazzale Aldo Moro 5, 00185, Roma, Italy

    Claudio Procesi

Authors
  1. Felix Huber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claudio Procesi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Felix Huber.

Additional information

FH acknowledges support by the Government of Spain (FIS2020-TRANQI and Severo Ochoa CEX2019-000910-S), Fundació Cellex, Fundació Mir-Puig, Generalitat de Catalunya (AGAUR SGR 1381 and CERCA), and the European Union under Horizon2020 (PROBIST 754510).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huber, F., Procesi, C. Tensor polynomial identities. Isr. J. Math. 247, 125–147 (2022). https://doi.org/10.1007/s11856-021-2262-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-021-2262-6

Search

Navigation