霍普夫代数与典型群的特征标
Hopf algebras and characters of classical groups
摘要：
Schur函数提供对称函数环的整基。通过确定适当的积、余积、单位、可数和对极及其性质，证明了该环具有自然的霍普夫代数结构.然后用Schur函数表示典型群GL（n），O（n）和Sp（n）的共变张量张量不可约表示的特征，并利用霍普夫代数确定群-子群分支规则和张量积的分解.分析是在n-独立的通用字符。对应的环CharGL、CharO和CharSp都有自己的自然霍普夫代数结构。在每种情况下识别适当的产品、副产品、单位、计数和对映体。
英文摘要：
Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their properties. Characters of covariant tensor irreducible representations of the classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur functions, and the Hopf algebra is exploited in the determination of group-subgroup branching rules and the decomposition of tensor products. The analysis is carried out in terms of n-independent universal characters. The corresponding rings, CharGL, CharO and CharSp, of universal characters each have their own natural Hopf algebra structure. The appropriate product, coproduct, unit, counit and antipode are identified in each case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
