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KRONECKER COEFFICIENTS VIA SYMMETRIC FUNCTIONS AND CONSTANT TERM IDENTITIES

ADRIANO GARSIA

Department of Mathematics, University of California San Diego, La Jolla, CA 92093-0112, USA

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NOLAN WALLACH

Department of Mathematics, University of California San Diego, La Jolla, CA 92093-0112, USA

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GUOCE XIN

Department of Mathematics, Capital Normal University, Beijing 100048, P. R. China

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, and

MIKE ZABROCKI

Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada

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https://doi.org/10.1142/S0218196712500221Cited by:5 (Source: Crossref)

Abstract

This work lies across three areas of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link led to the calculation of some Kronecker coefficients by computing constant terms and conversely the computations of certain constant terms by computing Kronecker coefficients by symmetric function methods. This led to results as well as methods for solving numerical problems in each of these separate areas.

Keywords:

AMSC: 05E05

References

G. E. Andrews, Mathematical Essays in Honor of Gian-Carlo Rota, eds. B. Sagan and R. Stanley (Birkhäuser, Boston, MA, 1998) pp. 1–22. Crossref, Google Scholar
A. M. Garsiaet al., Adv. Appl. Math. 42(3), 392 (2009). Crossref, Web of Science, Google Scholar
A. M. Garsia and J. Remmel, Graphs Combin. 1, 217 (1985). Crossref, Web of Science, Google Scholar
A. M. Garsiaet al., Discrete Math. 309(16), 5206 (2009). Crossref, Web of Science, Google Scholar
D. E. Littlewood, J. London Math. Soc. (1) 31, 89 (1956). Web of Science, Google Scholar
J.-G. Luque and J. Y. Thibon, Phys. Rev. A 67, 042303 (2003). Crossref, Web of Science, Google Scholar
J.-G. Luque and J. Y. Thibon, J. Phys. A 39, 371 (2006). Crossref, Google Scholar
I. G. Macdonald , Symmetric Functions and Hall Polynomials , 2nd edn. ( Oxford University Press , 1995 ) . Crossref, Google Scholar
F. D. Murnaghan, Amer. J. Math. 60, 761 (1938). Crossref, Web of Science, Google Scholar
T. Scharf, J. Y. Thibon and B. Wybourne, J. Phys. A 26, 7461 (1993). Crossref, Google Scholar
N. Wallach, Acta Appl. Math. 86(2), 203 (2005). Crossref, Web of Science, Google Scholar
N. Wallach, Representation Theory and Complex Analysis, Lectures given at the C.I.M.E. Summer School held in Venice, Italy June 10–17, 2004, Lecture Notes in Mathematics 1931 (Springer, 2008) pp. 345–376. Crossref, Google Scholar
G. Xin, The ring of Malcev–Neumann series and the residue theorem, Ph.D. Dissertation, Brandeis University (2004) . Google Scholar
G. Xin, Electron. J. Combin. 11, R53 (2004), arXiv:math.CO/0408377. Google Scholar