scholarly journals The Product of Two Involutions in the Unitary Group of a Hermitian Form

1971 ◽  
Vol 21 (5) ◽  
pp. 449-456 ◽  
Author(s):  
D. Djoković
Keyword(s):  
Unitary Group ◽  
Hermitian Form

scholarly journals The subnormal structure of classical-like groups over commutative rings

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raimund Preusser
Keyword(s):  
Unitary Group ◽  
Hermitian Form ◽  
Commutative Rings ◽  
Unitary Groups ◽  
Elementary Subgroup ◽  
Sandwich Theorem ◽  
Subnormal Structure ◽  
Form Ring ◽  
K 12 ◽  
Subnormal Subgroups

AbstractLet 𝑛 be an integer greater than or equal to 3, and let (R,\Delta) be a Hermitian form ring, where 𝑅 is commutative. We prove that if 𝐻 is a subgroup of the odd-dimensional unitary group \operatorname{U}_{2n+1}(R,\Delta) normalised by a relative elementary subgroup \operatorname{EU}_{2n+1}((R,\Delta),(I,\Omega)), then there is an odd form ideal (J,\Sigma) such that\operatorname{EU}_{2n+1}((R,\Delta),(JI^{k},\Omega_{\mathrm{min}}^{JI^{k}}\dotplus\Sigma\circ I^{k}))\leq H\leq\operatorname{CU}_{2n+1}((R,\Delta),(J,\Sigma)),where k=12 if n=3 respectively k=10 if n\geq 4. As a consequence of this result, we obtain a sandwich theorem for subnormal subgroups of odd-dimensional unitary groups.

scholarly journals A Herman–Avila–Bochi formula for higher-dimensional pseudo-unitary and Hermitian-symplectic cocycles

2014 ◽  
Vol 35 (5) ◽  
pp. 1582-1591 ◽  
Author(s):  
CHRISTIAN SADEL
Keyword(s):  
Lyapunov Exponents ◽  
Unitary Group ◽  
Symplectic Group ◽  
Hermitian Form ◽  
Schrödinger Operators ◽  
Parameter Family ◽  
Schrodinger Operators ◽  
Type Formula ◽  
Higher Dimensional

A Herman–Avila–Bochi type formula is obtained for the average sum of the top$d$Lyapunov exponents over a one-parameter family of$\mathbb{G}$-cocycles, where$\mathbb{G}$is the group that leaves a certain, non-degenerate Hermitian form of signature$(c,d)$invariant. The generic example of such a group is the pseudo-unitary group$\text{U}(c,d)$or, in the case$c=d$, the Hermitian-symplectic group$\text{HSp}(2d)$which naturally appears for cocycles related to Schrödinger operators. In the case$d=1$, the formula for$\text{HSp}(2d)$cocycles reduces to the Herman–Avila–Bochi formula for$\text{SL}(2,\mathbb{R})$cocycles.

scholarly journals PAIR CORRELATOR IN THE ITZYKSON-ZUBER INTEGRAL

1992 ◽  
Vol 07 (37) ◽  
pp. 3503-3507 ◽  
Author(s):  
A. MOROZOV
Keyword(s):  
Explicit Expression ◽  
Unitary Group ◽  
Pair Correlator

An explicit expression is suggested for the average [Formula: see text] over the unitary group SU (N) with the Itzykson-Zuber measure [dU] exp tr ΦUΨU†.

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