正交辛和酉超群上的不变积分
Invariant integration on orthosymplectic and unitary supergroups
摘要：
正交辛超群OSp（m| 2n）和酉超群U（p| q）的研究遵循一种新的方法，从Harish-Chandra对开始，并将Berezin等人的层理论超流形方法与Rogers等人的微分几何方法联系起来。李群G的基本表示的矩阵元用乘积超流形G_0 x R^{0| N}，其中G_0是G的基本李群，N是G的奇维数.这个积超流形同构于G的超流形。这导致了相应的李超代数g的标准生成元作为G上的不变导子的一个新的表达式。利用这些结果，给出了OSp（m）上不变积分的一个新的透明公式|2n）和U（p| q）得到。
英文摘要：
The orthosymplectic supergroup OSp(m|2n) and unitary supergroup U(p|q) are studied following a new approach that starts from Harish-Chandra pairs and links the sheaf-theoretical supermanifold approach of Berezin and others with the differential geometry approach of Rogers and others. The matrix elements of the fundamental representation of the Lie supergroup G are expressed in terms of functions on the product supermanifold G_0 x R^{0|N}, with G_0 the underlying Lie group and N the odd dimension of G. This product supermanifold is isomorphic to the supermanifold of G. This leads to a new expression for the standard generators of the corresponding Lie superalgebra g as invariant derivations on G. Using these results a new and transparent formula for the invariant integrals on OSp(m|2n) and U(p|q) is obtained.
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