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Boson-fermion correspondence — 2 results found.

      
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Comments Related to Infinite Wedge Representations
C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (1) 2017, pp. 13-35
Nathan Grieve (Received: 2016/06/30, Revised: 2016/11/07)

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We study the infinite wedge representation and show how it is related to the universal central extension of \(g[t,t^{-1}]\), the loop algebra of a complex semi-simple Lie algebra \(g\). We also give an elementary proof of the boson-fermion correspondence. Our approach to proving this result is based on a combinatorial construction combined with an application of the Murnaghan-Nakayama rule.

Nous étudions l’algèbre extérieure en dimension infinie et montrons comment elle est reliée à l’extension centrale universelle de \(g[t,\!t^{-1}]\), l’algèbre de lacets sur une algèbre de Lie \(g\) semi-simple complexe. De plus, nous donnons une preuve élémentaire de la correspondance boson-fermion. Pour ce faire, nous utilisons une construction combinatoire, ainsi que la règle de Murnaghan-Nakayama.

A geometric boson-fermion correspondence
C. R. Math. Rep. Acad. Sci. Canada Vol. 28 (3) 2006, pp. 65–84
Alistair Savage (Received: 2006/09/07)

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The fixed points of a natural torus action on the Hilbert schemes of points in \(\C^2\) are quiver varieties of type \(A_\infty\). The equivariant cohomology of the Hilbert schemes and quiver varieties can be given the structure of bosonic and fermionic Fock spaces respectively. Then the localization theorem, which relates the equivariant cohomology of a space with that of its fixed point set, yields a geometric realization of the important boson-fermion correspondence.

Les points fixes d’une action canonique d’un tore sur le schéma de Hilbert de \(\C^2\) sont des variétés de quiver de type \(A_\infty\). On peut donner la cohomologie équivariante des schémas de Hilbert et des variétés de quiver la structure des éspaces de Fock fermionique et bosonique, respectivement. Alors, la théorème de localisation, qui lie la cohomologie équivariante d’une éspace avec la cohomologie équivariante de son ensemble des point fixes, nous permet de donner une réalisation géométrique de la correspondance bosonique-fermionique.

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algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

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05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

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