JP Journal of Algebra, Number Theory and Applications
Volume 39, Issue 2, Pages 151 - 164
(April 2017) http://dx.doi.org/10.17654/NT039020151 |
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THE HECKE ALGEBRA REPRESENTATION OF THE COMPLEX REFLECTION GROUP IS UNITARY
Mohammad Y. Chreif and Mohammad N. Abdulrahim
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Abstract: We consider a 2-dimensional representation of the Hecke algebra where is the complex reflection group and u is the set ofindeterminates Afterspecializing the indeterminates to non-zero complex numbers on the unit circle, we prove that the representation is unitary relative to a Hermitian positive definite matrix. We then determine a necessary and sufficient condition for an element of to belong to the kernel of the complex specialization of the representation of the Hecke algebra
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Keywords and phrases: braid group, Hecke algebra, irreducible, reflections. |
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