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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Neoclassical invariant theory – some lost theorems – a mathematical chat; pp. 3–6

(Full article in PDF format) doi: 10.3176/proc.2010.1.02


Authors

Jaak Peetre

Abstract

In this short note I provide an account of some results and ideas, as well as a review of certain aspects and history of the invariant theory, linking it to multilinear forms, multidimensional matrices and geometry, and analysis of symmetric domains.

Keywords

invariants, covariants, multilinear forms, hyperdeterminants, symmetric domain.

References

  1. Cayley , A. On the theory of linear transformations. Cambridge Math. J. , 1845 , 4 , 193–209.

  2. Crilly , T. and Crilly , A. J. Arthur Cayley: Mathematician Laureate of the Victorian Age. JHU Press , 2006.

  3. Engliš , M. , Hille , S. C. , Rosengren , H. , and Zhang , G. A new kind of Hankel-Toeplitz type operator connected with the complementary series. Arab J. Math. Sci. , 2000 , 6 , 49–80.

  4. Fischer , E. S. Über die Cayleysche Eliminationsmethode. Math. Z. , 1927 , 26 , 497–550.
doi:10.1007/BF01475471

  5. Gel¢fand , I. M. , Kapranov , M. M. , and Zelevinsky , A. V. Discriminants , Resultants and Multidimensional Determinants. Birkhäuser , Boston , 1994.
doi:10.1007/978-0-8176-4771-1

  6. Lagrange , J.-L. Mécanique Analytique (Analytical Mechanics) (4. ed. , 2 vols. Paris: Gauthier-Villars et fils , 1888–89. First Edition: 1788.)

  7. Peetre , J. On Quaternary-Bibinary Forms. Manuscript , Kåseberga , August 31 , 1994.

  8. Peetre , J. , Rosengren , H. , and Zhang , G. Neoclassical Invariant Theory. New edition of 1998 version , 2007.

  9. Peetre , J. and Zhang , G. Harmonic analysis on the quantized Riemann sphere. Internat. J. Math. Math. Sci. , 1993 , 16 , 225–243.
doi:10.1155/S0161171293000274

10. Timmerding , H. E. Invariantentheorie. In Repertorium der höheren Mathematik. I. Analysis. Erste Hälfte. Algebra , Differential- und Integralrechnung (Pascal , E. , ed.). B. G. Teubner , Leipzig , 1910.
 
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Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December