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Fock space dualities
Journal of Mathematical Physics ( IF 1.3 ) Pub Date : 2020-08-01 , DOI: 10.1063/5.0015578
K. Neergård 1
Affiliation  

A general theorem due to Howe of dual action of a classical group and a certain non-associative algebra on a space of symmetric or alternating tensors is reformulated in a setting of second quantization, and familiar examples in atomic and nuclear physics are discussed. The special case of orthogonal-orthogonal duality is treated in detail. It is shown that, like it was done by Helmers more than half a century ago in the analogous case of symplectic-symplectic duality, one can base a proof of the orthogonal-orthogonal duality theorem and a precise characterization of the relation between the equivalence classes of the dually related irreducible representations on a calculation of characters by combining it with an analysis of the representation of a reflection. Young diagrams for the description of equivalence classes of irreducible representations of orthogonal Lie algebras are introduced. The properties of a reflection of the number non-conserving part in the dual relationship between orthogonal Lie algebras corroborate a picture of an almost perfect symmetry between the partners.

中文翻译:

福克空间二元性

在第二量子化的设置中重新表述了经典群和特定非结合代数在对称或交替张量空间上的双重作用的 Howe 的一般定理,并讨论了原子和核物理学中熟悉的例子。对正交-正交对偶的特殊情况进行了详细处理。结果表明,就像半个多世纪前 Helmers 在辛-辛对偶性的类似情况中所做的那样,人们可以基于正交-正交对偶性定理的证明和对等价类之间关系的精确表征通过将其与对反射表示的分析相结合,对字符计算的双重相关不可约表示进行了分析。介绍了描述正交李代数不可约表示的等价类的杨图。正交李代数之间的对偶关系中数非守恒部分的反射性质证实了伙伴之间几乎完美对称的图景。
更新日期:2020-08-01
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