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Zhijin Li - One of the best experts on this subject based on the ideXlab platform.

  • superconformal partial waves for stress tensor multiplet correlator in 4d mathcal n 2 scfts
    Journal of High Energy Physics, 2020
    Co-Authors: Zhijin Li
    Abstract:

    We compute the superconformal partial waves of the four-point correlator 〈JJJJ〉, in which the external Operator J is the superconformal primary of the 4D$$ \mathcal{N} $$ = 2 stress-tensor multiplet $$ \mathcal{J} $$. We develop the superembedding formalism for the superconformal field theories (SCFTs) with extended supersymmetry. In $$ \mathcal{N} $$ = 2 SCFTs, the three- point functions $$ \left\langle \mathcal{JJO}\right\rangle $$ with general multiplet $$ \mathcal{O} $$ contain two independent nilpotent superconformal invariants and new superconformal tensor structures, which can be nicely constructed from variables in superembedding space, and the three-point functions can be written in compact forms. We compute the superconformal partial waves corresponding to the exchange of long multiplets using supershadow approach. The results are consistent with the non-trivial constraints by decomposing the $$ \mathcal{N} $$ = 2 superconformal blocks into $$ \mathcal{N} $$ = 1 superconformal blocks. Our results provide the necessary ingredient to study the fascinating 4D$$ \mathcal{N} $$ = 2 SCFTs using conformal bootstrap.

  • superconformal partial waves for stress tensor multiplet correlator in 4d mathcal n 2 scfts
    arXiv: High Energy Physics - Theory, 2018
    Co-Authors: Zhijin Li
    Abstract:

    We compute the superconformal partial waves of the four-point correlator $\langle JJJJ\rangle$, in which the external Operator $J$ is the superconformal primary of the $4D$ $\mathcal{N}=2$ stress-tensor multiplet $\mathcal{J}$. We develop the superembedding formalism for the superconformal field theories (SCFTs) with extended supersymmetry. In $\mathcal{N}=2$ SCFTs, the three-point functions $\langle \mathcal{J}\mathcal{J}\mathcal{O}\rangle$ with general multiplet $\mathcal{O}$ contain two independent nilpotent superconformal invariants and new superconformal tensor structures, which can be nicely constructed from variables in superembedding space, and the three-point functions can be solved in compact forms. We compute the superconformal partial waves corresponding to the exchange of long multiplets using supershadow approach. The results are consistent with the non-trivial constraints by decomposing the $\mathcal{N}=2$ superconformal blocks into $\mathcal{N}=1$ superconformal blocks. Our results provide the necessary ingredient to study the fascinating $4D$ $\mathcal{N}=2$ SCFTs using conformal bootstrap.

Maxim Nazarov - One of the best experts on this subject based on the ideXlab platform.

  • a mixed hook length formula for affine hecke algebras
    European Journal of Combinatorics, 2004
    Co-Authors: Maxim Nazarov
    Abstract:

    Let H^l be the affine Hecke algebra corresponding to the group GLl over a p-adic field with residue field of cardinality q. We will regard H^l as an associative algebra over the field C(q). Consider the H^l+m-module W induced from the tensor product of the evaluation modules over the algebras H^l and H^m. The module W depends on two partitions λ of l and µ of m, and on two non-zero elements of the field C(q). There is a canonical Operator J acting on W; it corresponds to the trigonometric R-matrix. The algebra H^l+m contains the finite dimensional Hecke algebra Hl+m as a subalgebra, and the Operator J commutes with the action of this subalgebra on W. Under this action, W decomposes into irreducible subspaces according to the Littlewood-Richardson rule. We compute the eigenvalues of J, corresponding to certain multiplicity-free irreducible components of W. In particular, we give a formula for the ratio of two eigenvalues of J, corresponding to the "highest" and the "lowest" components. As an application, we derive the well known q-analogue of the hook-length formula for the number of standard tableaux of shape λ.

  • mixed hook length formula for degenerate a fine hecke algebras
    arXiv: Representation Theory, 2003
    Co-Authors: Maxim Nazarov
    Abstract:

    Take the degenerate a fine Hecke algebra H l+m corresponding to the group GL l +m over a p-adic field.Consider the H l+m -module W induced from the tensor product of the evaluation modules over the algebras H l x and H m .The module W depends on two partitions λ of l and μ of m, and on two complex numbers.There is a canonical Operator J acting in W, it corresponds to the Yang R-matrix.The algebra H l+m contains the symmetric group algebra ℂ S l +m as a subalgebra, and J commutes with the action of this subalgebra in W. Under this action,W decomposes into irreducible subspaces according to the Littlewood — Richardson rule. We compute the eigenvalues of J, corresponding to certain multiplicity-free irreducible components of W. In particular,we give a formula for the ratio of two eigenvalues of J, corresponding to the maximal and minimal irreducible components. As an application of our results,we derive the well-known hook-length formula for the dimension of the irreducible ℂ S l -module corresponding to λ.

  • on irreducibility of tensor products of yangian modules associated with skew young diagrams
    Duke Mathematical Journal, 2002
    Co-Authors: Maxim Nazarov, Vitaly Tarasov
    Abstract:

    We study the tensor product $W$ of any number of irreducible finite-dimensional modules $V\sb 1,\ldots V\sb k$ over the Yangian ${\rm Y}(\mathfrak {gl}\sb N)$ of the general linear Lie algebra $\mathfrak {gl}\sb N$. For any indices $i,J=1,\ldots k$, there is a canonical nonzero intertwining Operator $J\sb {iJ} : V\sb i\otimes V\sb J\to V\sb J\otimes V\sb i$. It has been conJectured that the tensor product $W$ is irreducible if and only if all Operators $J\sb {iJ}$ with $i<J$ are invertible. We prove this conJecture for a wide class of irreducible ${\rm Y}(\mathfrak {gl}\sb N)$-modules $V\sb 1,\ldots V\sb k$. Each of these modules is determined by a skew Young diagram and a complex parameter. We also introduce the notion of a Durfee rank of a skew Young diagram. For an ordinary Young diagram, this is the length of its main diagonal.

Debmalya Sain - One of the best experts on this subject based on the ideXlab platform.

G R Jin - One of the best experts on this subject based on the ideXlab platform.

  • high precision evaluation of wigner s d matrix by exact diagonalization
    Physical Review E, 2015
    Co-Authors: X M Feng, P Wang, W Yang, G R Jin
    Abstract:

    The precise calculations of Wigner's d matrix are important in various research fields. Due to the presence of large numbers, direct calculations of the matrix using Wigner's formula suffer from a loss of precision. We present a simple method to avoid this problem by expanding the d matrix into a complex Fourier series and calculate the Fourier coefficients by exactly diagonalizing the angular momentum Operator J(y) in the eigenbasis of J(z). This method allows us to compute the d matrix and its various derivatives for spins up to a few thousand. The precision of the d matrix from our method is about 10(-14) for spins up to 100.

Llopez E. Cosme - One of the best experts on this subject based on the ideXlab platform.

  • A characterization of the n-ary many-sorted closure Operators and a many-sorted Tarski irredundant basis theorem
    Taylor & Francis, 2019
    Co-Authors: Vidal J. Climent, Llopez E. Cosme
    Abstract:

    A theorem of single-sorted algebra states that, for a closure space (A, J) and a natural number n, the closure Operator J on the set A is n-ary if and only if there exists a single-sorted signature Σ and a Σ-algebra A such that every operation of A is of an arity ≤ n and J = SgA, where SgA is the subalgebra generating Operator on A determined by A. On the other hand, a theorem of Tarski asserts that if J is an n-ary closure Operator on a set A with n ≥ 2, then, for every i, J ∈ IrB(A, J), where IrB(A, J) is the set of all natural numbers which have the property of being the cardinality of an irredundant basis (≡ minimal generating set) of A with respect to J, if i < J and {i+ 1, . . . , J −1} ∩IrB(A, J) = ∅, then J −i ≤ n−1. In this article we state and prove the many-sorted counterparts of the above theorems. But, we remark, regarding the first one under an additional condition: the uniformity of the many-sorted closure Operator.  Key words: S-sorted set, delta of Kronecker, support of an S-sorted set, n-ary manysorted closure Operator, uniform many-sorted closure Operator, irredundant basis with respect to a many-sorted closure Operator