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Super boson-fermion correspondence

Victor G. Kac, J. W. Van de Leur (1987)

Annales de l'institut Fourier

We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential non-commutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra g ˜ l 1 | 1 . The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex operator constructions...

Symmetric identity for polynomial sequences satisfying A n + 1 ' ( x ) = ( n + 1 ) A n ( x )

Farid Bencherif, Rachid Boumahdi, Tarek Garici (2021)

Communications in Mathematics

Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A n + 1 ' ( x ) = ( n + 1 ) A n ( x ) with A 0 ( x ) a constant polynomial. This identity allows us to obtain in a simple way some known relations involving Apostol-Bernoulli polynomials, ApostolEuler polynomials and generalized Bernoulli polynomials attached to a primitive Dirichlet character.

The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications

Guo-Niu Han (2010)

Annales de l’institut Fourier

The paper is devoted to the derivation of the expansion formula for the powers of the Euler Product in terms of partition hook lengths, discovered by Nekrasov and Okounkov in their study of the Seiberg-Witten Theory. We provide a refinement based on a new property of t -cores, and give an elementary proof by using the Macdonald identities. We also obtain an extension by adding two more parameters, which appears to be a discrete interpolation between the Macdonald identities and the generating function...

The number of complete exceptional sequences for a Dynkin algebra

Mustafa Obaid, Khalid Nauman, Wafa S. M. Al-Shammakh, Wafaa Fakieh, Claus Michael Ringel (2013)

Colloquium Mathematicae

The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type Δ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.

Currently displaying 301 – 320 of 353