Celebratio Mathematica — Singer — Complete Bibliography

Complete Bibliography

Works connected to Orlando Alvarez

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O. Alvarez, I. M. Singer, and B. Zumino: “Gravitational anomalies and the family’s index theorem,” Comm. Math. Phys. 96 : 3 (1984), pp. 409–417. MR 769356 Zbl 0587.58042 article

Bruno Zumino	Related
Orlando Alvarez	Related

O. Alvarez, I. M. Singer, and P. Windey: “Quantum mechanics and the geometry of the Weyl character formula,” Nuclear Phys. B 337 : 2 (June 1990), pp. 467–486. MR 1057724 article

General field theoretic methods are developed which will allow a path integral derivation of the character formula for loop groups. The methods are introduced in the classical Weyl character case. The irreducible representations of a compact semi-simple Lie group \( G \) are realized as the ground states of a supersymmetric quantum mechanical system. The Hilbert space for the quantum mechanical system is the space of sections of a holomorphic line bundle \( L \) over the complex manifold \( G/T \), where \( T \) is the maximal torus of \( G \). The Weyl character formula is derived by an explicit path integral computation of the index of the Dolbeault operator.

Orlando Alvarez	Related
Paul Windey	Related

O. Alvarez, I. M. Singer, and P. Windey: “The supersymmetric \( \sigma \)-model and the geometry of the Weyl–Kač character formula,” Nuclear Phys. B 373 : 3 (April 1992), pp. 647–687. MR 1159678 ArXiv hep-th/9109047 article

Orlando Alvarez	Related
Paul Windey	Related

O. Alvarez and I. M. Singer: “Beyond the elliptic genus,” Nuclear Phys. B 633 : 3 (July 2002), pp. 309–344. MR 1910266 Zbl 0995.58016 article

O. Alvarez and I. M. Singer: “Beyond the string genus,” Nuclear Phys. B 850 : 2 (September 2011), pp. 349–386. MR 2803587 Zbl 1229.81212 article