On the spinor norm

1962 ◽  
Vol 13 (1) ◽  
pp. 434-451 ◽  
Author(s):  
Hans Zassenhaus
Keyword(s):  
Spinor Norm

A new formula for the spinor norm

1978 ◽  
Vol 19 (6) ◽  
pp. 1265-1266 ◽  
Author(s):  
M. Perroud
Keyword(s):  
Spinor Norm ◽  
New Formula

scholarly journals Integral spinor norm groups over dyadic local fields

2003 ◽  
Vol 102 (1) ◽  
pp. 125-182 ◽  
Author(s):  
Constantin N. Beli
Keyword(s):  
Local Fields ◽  
Spinor Norm

scholarly journals Spinor norm for skew-hermitian forms over quaternion algebras

2015 ◽  
Vol 151 ◽  
pp. 159-171
Author(s):  
Luis Arenas-Carmona ◽  
Patricio Quiroz
Keyword(s):  
Quaternion Algebras ◽  
Hermitian Forms ◽  
Spinor Norm

Tubes, Cohomology with Growth Conditions and an Application to the Theta Correspondence

1988 ◽  
Vol 40 (1) ◽  
pp. 1-37 ◽  
Author(s):  
Stephen S. Kudla ◽  
John J. Millson
Keyword(s):  
Finite Volume ◽  
Symmetric Spaces ◽  
Integral Formula ◽  
Growth Conditions ◽  
Harmonic Forms ◽  
Theta Correspondence ◽  
Locally Symmetric Spaces ◽  
Spinor Norm ◽  
Integer Coefficients ◽  
Locally Symmetric Space

In this paper we continue our effort [11], [12], [13], [14] to interpret geometrically the harmonic forms on certain locally symmetric spaces constructed by using the theta correspondence. The point of this paper is to prove an integral formula, Theorem 2.1, which will allow us to generalize the results obtained in the above papers to the finite volume case (the previous papers treated only the compact case). We then apply our integral formula to certain finite volume quotients of symmetric spaces of orthogonal groups. The main result obtained is Theorem 4.2 which is described below. We let (,) denote the bilinear form associated to a quadratic form with integer coefficients of signature (p, q). We assume that the fundamental group Γ ⊂ SO(p, q) of our locally symmetric space is the subgroup of the integral isometries of (,) congruent to the identity matrix modulo some integer N. We assume that N is chosen large enough so that Γ is neat (the multiplicative subgroup of C* generated by the eigenvalues of the elements of Γ has no torsion), Borel [2], 17.1 and that every element in Γ has spinor norm 1, Millson-Raghunathan [15], Proposition 4.1. These conditions are needed to ensure that our cycles Cx (see below) are orientable. The methods we will use apply also to unitary and quaternion unitary locally symmetric spaces, see [13].

Groups, Discriminants and the Spinor Norm

1989 ◽  
Vol 21 (1) ◽  
pp. 51-56
Author(s):  
Geoffrey Mason
Keyword(s):  
Spinor Norm
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