Reversible complex hyperbolic isometries

Gongopadhyay, Krishnendu; Parker, John R.

doi:10.1016/j.laa.2012.11.029

Cited by 13 publications

(12 citation statements)

References 26 publications

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“…Gongopadhyay and Parker [5] and Gongopadhyay, Parker and Parsad [6] classified the dynamical action in SU(p,q) using the coefficients of their characteristic polynomial. In the case p+q = 4, the characteristic polynomial is…”

Section: Monic Self-inversive Polynomialsmentioning

confidence: 99%

Discriminants of a Class of Self-inversive Polynomials and Real Binary Forms

Uchimura

2017

Preprint

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A class of self-inversive polynomials includes all the self-reciprocal polynomials. Let A denote the set of all self-reciprocal polynomials with n+1 coefficients. Let B denote the set of certain self-inversive and non self-reciprocal polynomials with n+1 coefficients for odd n. Let C denote the set of real binary n-ic forms. Then there exist a bijection between A and C and another bijection between B and C. Let f be a monic polynomial in A and g be the corresponding polynomial in C. If the reading coefficient of g is not zero, then the discriminant of g is expressed by the determinant of a matrix of type (n, n). Any element of the matrix is a polynomial in the coefficients of f with integer coefficients. The same holds for monic polynomials in B.

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Section: Monic Self-inversive Polynomialsmentioning

confidence: 99%

Discriminants of a Class of Self-inversive Polynomials and Real Binary Forms

Uchimura

2017

Preprint

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“…Conversely, if g is similar to its inverse via an involution h, then g = h(g −1 h) is a decomposition of g into products of two involutions. The elements of a group such as in the preceding are called strongly reversible [13]. We now characterize the strongly reversible elements of the symplectic group P 2n .…”

Section: On Products Of Symplectic Involutionsmentioning

confidence: 99%

Each symplectic matrix is a product of four symplectic involutions

Cruz

2015

Linear Algebra and its Applications

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Available online xxxx Submitted by V.V. Sergeichuk MSC: 15A21 15A23 Keywords: Symplectic matrices Involutions Coninvolutions Square zero matrices Hamiltonian matricesGustafson, Halmos, and Radjavi in 1973 proved that each matrix A with det A = ±1 is a product of four involutions. We prove that these involutions can be taken to be symplectic if A is symplectic (every symplectic matrix has unit determinant). Using this result we give an alternative proof of Laffey's theorem that every nonsingular even size matrix is a product of skew symmetric matrices. Ballantine in 1978 proved that each matrix A with | det A| = 1 is a product of four coninvolutions. We prove that these coninvolutions can be taken to be symplectic if A is symplectic. We also prove that each Hamiltonian matrix is a sum of two square zero Hamiltonian matrices.

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“…The reversibility of isometries of the complex hyperbolic space has been investigated by Gongopadhyay and Parker in [GP13]. The group U(n, 1) and SU(n, 1) act as the holomorphic isometries of the n-dimensional complex hyperbolic space H n C .…”

Section: Introductionmentioning

confidence: 99%

“…The group U(n, 1) and SU(n, 1) act as the holomorphic isometries of the n-dimensional complex hyperbolic space H n C . Reversible elements in these groups were classified in [GP13]. It follows from this work that an element g in U(n, 1) is reversible if and only if it is strongly reversible.…”

Section: Introductionmentioning

confidence: 99%

Reversible quaternionic hyperbolic isometries

Bhunia

Gongopadhyay

2020

Linear Algebra and its Applications

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Let G be a group. An element g ∈ G is called reversible if it is conjugate to g −1 within G, and called strongly reversible if it is conjugate to g −1 by an order two element of G. Let H n H be the n-dimensional quaternionic hyperbolic space. Let PSp(n, 1) be the isometry group of H n H . In this paper, we classify reversible and strongly reversible elements in Sp(n) and Sp(n, 1). Also, we prove that all the elements of PSp(n, 1) are strongly reversible.

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Reversible complex hyperbolic isometries

Cited by 13 publications

References 26 publications

Discriminants of a Class of Self-inversive Polynomials and Real Binary Forms

Discriminants of a Class of Self-inversive Polynomials and Real Binary Forms

Each symplectic matrix is a product of four symplectic involutions

Reversible quaternionic hyperbolic isometries

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