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R. Coquereaux, C. McSwiggen and J.-B. Zuber, On Horn’s Problem and its Volume Function, Commun.Math.Phys.(2019),
Original
1904
Earlier work this paper cites.
C. McSwiggen, Box splines, tensor product multiplicities and the volume function,
Original
1909
Earlier work this paper cites.
A. Berenstein and A. Zelevinsky,
1992
Earlier work this paper cites.
Lie Package, Marc A. A. van Leeuwen, Arjeh M. Cohen, Bert Lisser, Computer Algebra Nederland, Amsterdam, ISBN 90-74116-02-7, 1992
1992
Earlier work this paper cites.
P. Di Francesco, P. Mathieu and D. Sénéchal,
1997
Earlier work this paper cites.
A. Knutson, T. Tao, The honeycomb model of GL(n) tensor products I: Proof of the saturation conjecture,
1999
Earlier work this paper cites.
R. Coquereaux and J.-B. Zuber. On Schur problem and Kostka numbers. To appear in Integrability, Quantization, and Geometry - B.A. Dubrovin memorial volume, edited by I. Krichever, S. Novikov, O. Ogievetsky and S. Shlosman, AMS, Proceedings of Symposia in Pure Mathematics (PSPUM) book series arXiv:2001.08046(2020),
Original
2001
Earlier work this paper cites.

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R. Coquereaux and J.-B. Zuber, Conjugation properties of tensor product multiplicities, J. Phys. A: Math. Theor. 47 (2014) 455202 (28pp) doi:10.1088/1751-8113/47/45/455202,
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R. Coquereaux and J.-B. Zuber, From orbital measures to Littlewood–Richardson coefficients and hive polytopes,
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R. Coquereaux and J.-B. Zuber. The Horn Problem for Real Symmetric and Quaternionic Self-Dual Matrices. SIGMA 15 (2019), 029, (34 pp)
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Later among the works it cites.
S.J. Jeralds, Private communication (2020)
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Closest in time.

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2020

Multiplicities, pictographs, and volumes

Coquereaux, Robert

Understand

The present contribution is the written counterpart of a talk given in Yerevan at the SQS'2019 International Workshop "Supersymmetries and Quantum Symmetries" (SQS'2019, 26 August - August 31, 2019).

After a short presentation of various pictographs (O-blades, metric honeycombs) that one can use in order to calculate SU(n) multiplicities (Littlewood-Richardson coefficients, Kostka numbers), we briefly discuss the semi-classical limit of these multiplicities in relation with the Horn and Schur volume functions and with the so-called Rn-polynomials that enter the expression of volume functions.
For n < 7 the decomposition of the Rn-polynomials on Lie group characters is already known, the case n=7 is obtained here.

Built on

R. Coquereaux, C. McSwiggen and J.-B. Zuber, On Horn’s Problem and its Volume Function, Commun.Math.Phys.(2019),
Original
1904
Earlier work this paper cites.
C. McSwiggen, Box splines, tensor product multiplicities and the volume function,
Original
1909
Earlier work this paper cites.
A. Berenstein and A. Zelevinsky,
1992
Earlier work this paper cites.
Lie Package, Marc A. A. van Leeuwen, Arjeh M. Cohen, Bert Lisser, Computer Algebra Nederland, Amsterdam, ISBN 90-74116-02-7, 1992
1992
Earlier work this paper cites.
P. Di Francesco, P. Mathieu and D. Sénéchal,
1997
Earlier work this paper cites.
A. Knutson, T. Tao, The honeycomb model of GL(n) tensor products I: Proof of the saturation conjecture,
1999
Earlier work this paper cites.
R. Coquereaux and J.-B. Zuber. On Schur problem and Kostka numbers. To appear in Integrability, Quantization, and Geometry - B.A. Dubrovin memorial volume, edited by I. Krichever, S. Novikov, O. Ogievetsky and S. Shlosman, AMS, Proceedings of Symposia in Pure Mathematics (PSPUM) book series arXiv:2001.08046(2020),
Original
2001
Earlier work this paper cites.

Similar

A. Knutson and T. Tao, Honeycombs and sums of Hermitian matrices,
2001
Cited alongside, same era.
H. Derksen and J. Weyman, On the Littelwood–Richardson polynomials,
2002
Cited alongside, same era.
E. Rassart, A Polynomiality Property for Littlewood–Richardson Coefficients,
2004
Cited alongside, same era.
T.B. McAllister, Degrees of stretched Kostka coefficients, DOI 10.1007/s10801-007-0083-2, J. Algebr. Comb. (2008) 27: 263-273
2008
Cited alongside, same era.
A. Ocneanu, 2009, private communication
2009
Cited alongside, same era.
Mathematica, Wolfram Research, Inc., Champaign, IL, 2012,
2012
Cited alongside, same era.

Then

R. Coquereaux and J.-B. Zuber, Conjugation properties of tensor product multiplicities, J. Phys. A: Math. Theor. 47 (2014) 455202 (28pp) doi:10.1088/1751-8113/47/45/455202,
Original
2014
Later among the works it cites.
A. Ocneanu. Harvard Lectures (2018). Video file L13 Adrian Ocneanu Harvard Physics 267 2017 10 02,
2017
Later among the works it cites.
R. Coquereaux and J.-B. Zuber, From orbital measures to Littlewood–Richardson coefficients and hive polytopes,
Original
2018
Later among the works it cites.
R. Coquereaux and J.-B. Zuber. The Horn Problem for Real Symmetric and Quaternionic Self-Dual Matrices. SIGMA 15 (2019), 029, (34 pp)
Original
2019
Later among the works it cites.
S.J. Jeralds, Private communication (2020)
2020
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

R. Coquereaux, Mathematica packages ”obladesSUn” and ”honeycombsSUn”, available on the web page

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P. Etingof and E. Rains, Mittag–Leffler type sums associated with root systems,

Original

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C. McSwiggen, Theory and Applications of Harish-Chandra Integrals, PhD thesis, Brown University, Providence, RI (2020, in preparation)

2020

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