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The Schur index and roots of unity [PDF]
Proceedings of the American Mathematical Society, 1972 A short proof is given for the main step in the proof of the theorem of Benard and Schacher which asserts that if the Schur index of a character χ \chi of a finite group is m then the mth roots of unity lie in the field of values Q ( χ ) Q(\chi ) .
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The exact Schur index in closed form
Physical Review D, 2021 The Schur limit of the superconformal index of a four-dimensional N = 2 superconformal field theory encodes rich physical information about the protected spectrum of the theory. For a Lagrangian model, this limit of the index can be computed by a contour integral of a multivariate elliptic function.
Pan, Yiwen, Peelaers, Wolfger
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Infrared Computations of Defect Schur Indices [PDF]
, 2016 We conjecture a formula for the Schur index of N=2 four-dimensional theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations ...
Cordova, Clay +2 more
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Passive discrete-time systems with a Pontryagin state space [PDF]
, 2019 Passive discrete-time systems with Hilbert spaces as an incoming and outgoing space and a Pontryagin space as a state space are investigated. A geometric characterization when the index of the transfer function coincides with the negative index of the ...
Lilleberg, Lassi
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Multivariate generalizations of the Foata-Schützenberger equidistribution [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 A result of Foata and Schützenberger states that two statistics on permutations, the number of inversions and the inverse major index, have the same distribution on a descent class.
Florent Hivert +2 more
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Transition between characters of classical groups, decomposition of Gelfand-Tsetlin patterns and last passage percolation [PDF]
, 2020 We study the combinatorial structure of the irreducible characters of the classical groups ${\rm GL}_{n}(\mathbb{C})$, ${\rm SO}_{2n+1}(\mathbb{C})$, ${\rm Sp}_{2n}(\mathbb{C})$, ${\rm SO}_{2n}(\mathbb{C})$ and the "non-classical" odd symplectic group ${\
Bisi, Elia, Zygouras, Nikos
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Journal of High Energy Physics, 2022 There is a well-known map from 4d N $$ \mathcal{N} $$ = 2 superconformal field theories (SCFTs) to 2d vertex operator algebras (VOAs). The 4d Schur index corresponds to the VOA vacuum character, and must be a solution with integral coefficients of a ...
Justin Kaidi +3 more
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An extension of MacMahon's Equidistribution Theorem to ordered multiset partitions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A classical result of MacMahon states that inversion number and major index have the same distribution over permutations of a given multiset. In this work we prove a strengthening of this theorem originally conjectured by Haglund.
Andrew Timothy Wilson
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Logarithmic W-algebras and Argyres-Douglas theories at higher rank
Journal of High Energy Physics, 2018 Families of vertex algebras associated to nilpotent elements of simply-laced Lie algebras are constructed. These algebras are close cousins of logarithmic W-algebras of Feigin and Tipunin and they are also obtained as modifications of semiclassical ...
Thomas Creutzig
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On a modular property of N=2 superconformal theories in four dimensions
, 2012 In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 ...
A Gadde +19 more
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