2022
DOI: 10.1007/s00006-022-01215-1
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The Orthogonal Branching Problem for Symplectic Monogenics

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Cited by 3 publications
(3 citation statements)
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“…Note that so(m) is generated by the operators X jk − X kj for 1 ≤ j < k ≤ m, giving rise to the well-known angular operators ubiquitous in quantum mechanics (often denoted by L ab with 1 ≤ a < b ≤ m). In our previous paper [3], we therefore tackled the next case k = 1 as this is a natural generalisation of said Fischer decomposition. The main problem with our branching rule (Theorem 5.6 in [3]) is the fact that these so(m)-spaces appear with infinite multiplicities, which are not always easy to keep track of.…”
Section: The Symplectic Dirac Operator and Monogenicsmentioning
confidence: 99%
See 1 more Smart Citation
“…Note that so(m) is generated by the operators X jk − X kj for 1 ≤ j < k ≤ m, giving rise to the well-known angular operators ubiquitous in quantum mechanics (often denoted by L ab with 1 ≤ a < b ≤ m). In our previous paper [3], we therefore tackled the next case k = 1 as this is a natural generalisation of said Fischer decomposition. The main problem with our branching rule (Theorem 5.6 in [3]) is the fact that these so(m)-spaces appear with infinite multiplicities, which are not always easy to keep track of.…”
Section: The Symplectic Dirac Operator and Monogenicsmentioning
confidence: 99%
“…In our previous paper [3], we therefore tackled the next case k = 1 as this is a natural generalisation of said Fischer decomposition. The main problem with our branching rule (Theorem 5.6 in [3]) is the fact that these so(m)-spaces appear with infinite multiplicities, which are not always easy to keep track of. Therefore the main goal of this paper is to show that one can organise these in an algebraic framework which extends to other values for k too, using a certain quadratic algebra.…”
Section: The Symplectic Dirac Operator and Monogenicsmentioning
confidence: 99%
“…the symplectic form ω) with derivatives. This gives rise to 038.1 the Dirac operator ∂ x = n k=1 e k ∂ x k where {e j , e k } = −2δ i j and the symplectic Dirac operator n k=1 iq k ∂ y k − ∂ q k ∂ x k where [∂ q j , iq k ] = iδ jk are the Heisenberg relations (see [1,2,4]).…”
Section: Introductionmentioning
confidence: 99%