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We study the relationship between the tensor product multiplicities of a compact semisimple Lie algebra $\mathfrak{g}$ and a special function $\mathcal{J}$ associated to $\mathfrak{g}$, called the volume function.
1904
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T. Bliem, On weight multiplicities of complex simple Lie algebras, PhD Thesis, Universität zu Köln (2008)
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2002
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H. Prautzsch, W. Boehm, M. Paluszny, Box splines, in Handbook of Computer Aided Geometric Design
2002
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M. Vergne, Quantification géométrique et réduction symplectique, Astérisque
2002
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2003
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A. Szenes, M. Vergne, Residue formulae for vector partitions and Euler-MacLaurin sums, Adv. Appl. Math
2003
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S. Billey, V. Guillemin, E. Rassart, A vector partition function for the multiplicities of 𝔰 𝔩 k ℂ \mathfrak{sl}_{k}{\mathbb{C}} , J. Algebra
2004
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R.C. King, C. Tollu, F. Toumazet, Stretched Littlewood–Richardson and Kostka coefficients, CRM Proceedings and Lecture Notes
2004
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2013
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M. Vergne, Poisson summation formula and box splines (2013), arXiv:1302.6599
2013
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2018
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P. Etingof, E. Rains, Mittag–Leffler type sums associated with root systems (2018), arXiv:1811.05293
2018
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2018
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2018
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A. Knutson, personal communication (2019)
2019
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