Evaluation and spanning sets of confluent Vandermonde forms

@article{Sunko2022EvaluationAS,
  title={Evaluation and spanning sets of confluent Vandermonde forms},
  author={Denis K. Sunko},
  journal={Journal of Mathematical Physics},
  year={2022}
}
  • D. Sunko
  • Published 1 August 2022
  • Mathematics
  • Journal of Mathematical Physics
An arbitrary derivative of a Vandermonde form in N variables is given as [ n1⋯ n N], where the ith variable is differentiated N − n i − 1 times, 1 ≤ n i ≤ N − 1. A simple decoding table is introduced to evaluate it by inspection. The special cases where 0 ≤ n i+1 − n i ≤ 1 for 0 < i < N are in one-to-one correspondence with ribbon Young diagrams. The respective N! standard ribbon tableaux map to a complete graded basis in the space of S N-harmonic polynomials. The mapping is realized as an… 
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References

SHOWING 1-10 OF 13 REFERENCES

Combinatorics, symmetric functions, and Hilbert schemes

We survey the proof of a series of conjectures in combinatorics using new results on the geometry of Hilbert schemes. The combinatorial results include the positivity conjecture for Macdonald’s…

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Finite Unitary Reflection Groups

Any finite group of linear transformations on n variables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of…

Grobner Bases and Invariant Theory

Solution of Vandermonde Systems of Equations

We obtain in this paper a considerable improvement over a method developed earlier by Ballester and Pereyra for the solution of systems of linear equations with Vandermonde matrices of coefficients.…

Elementary Theory: the Incompressible Quantum Fluid

In this lecture, I shall outline what I believe to be the correct fundamental picture of the fractional quantum Hall effect. The principal features of this picture are that the 1/3 state and its…

Multivariate diagonal coinvariant spaces for complex reflection groups

Generic example of algebraic bosonisation

Two identical non-interacting fermions in a three-dimensional harmonic oscillator well are bosonised exactly according to a recently developed general algebraic scheme. Rotational invariance is taken…

Natural generalization of the ground-state Slater determinant to more than one dimension

The basic question is addressed of how the space dimension d is encoded in the Hilbert space of N identical fermions. There appears a finite number N!