On Extensions of Affine Vertex Algebras at Half-Integer Levels

2017 ◽  
pp. 281-298
Author(s):  
Dražen Adamović ◽  
Ozren Perše
Keyword(s):  
Vertex Algebras ◽  
Half Integer

scholarly journals CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK

2010 ◽  
Vol 06 (02) ◽  
pp. 281-309 ◽  
Author(s):  
F. G. GARVAN
Keyword(s):  
Partition Function ◽  
Rank Function ◽  
Maass Forms ◽  
Hecke Eigenforms ◽  
Half Integer ◽  
Integer Weight

Let spt (n) denote the total number of appearances of smallest parts in the partitions of n. Recently, Andrews showed how spt (n) is related to the second rank moment, and proved some surprising Ramanujan-type congruences mod 5, 7 and 13. We prove a generalization of these congruences using known relations between rank and crank moments. We obtain explicit Ramanujan-type congruences for spt (n) mod ℓ for ℓ = 11, 17, 19, 29, 31 and 37. Recently, Bringmann and Ono proved that Dyson's rank function has infinitely many Ramanujan-type congruences. Their proof is non-constructive and utilizes the theory of weak Maass forms. We construct two explicit nontrivial examples mod 11 using elementary congruences between rank moments and half-integer weight Hecke eigenforms.

scholarly journals Associating quantum vertex algebras to Lie algebragl∞

2014 ◽  
Vol 399 ◽  
pp. 1086-1106 ◽  
Author(s):  
Cuipo Jiang ◽  
Haisheng Li
Keyword(s):  
Vertex Algebras ◽  
Quantum Vertex

Rotor-Encoded Heteronuclear MQ MAS NMR Spectroscopy of Half-Integer Quadrupolar and Spin I=1/2 Nuclei

2002 ◽  
Vol 154 (1) ◽  
pp. 101-129 ◽  
Author(s):  
Adonis Lupulescu ◽  
Steven P. Brown ◽  
Hans Wolfgang Spiess
Keyword(s):  
Nmr Spectroscopy ◽  
Mas Nmr ◽  
Half Integer
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