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Results tagged with rt.representation-theory
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user 40782
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
1
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Spinors on orbifolds
In Euclidean case one should consider $n = 4\,m$ and in pseudo-Euclidean case $n = 4\,m - 2$, where $m = 1, 2, 3, \dots$ In this case the half of parallel spinors (of the same chirality) will be cut …
- 371
7
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1
answer
467
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Spin manifolds with one parallel spinor
Are there any examples of D-dimensional Ricci-flat Riemannian (spin) manifolds of dimension D= 2,3,4,5 with the dimension of the space of parallel spinors equal to 1? And the same question for the pse …
- 371
1
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0
answers
83
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Extra-Lorentzian Kac-Moody algebras
My question is about Kac-Moody (KM) algebras of finite rank with symmetrized Cartan matrices $B = C A$ ($A$ is Cartan matrix) of signatures $(-,-,+,...,+)$, $(-,-,-,+,...,+)$, etc. i.e. with $2$ …
- 371
0
votes
1
answer
244
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The integer structure of twice inverse of Cartan matrix and $Z_2$-group of symmetry of Dynki...
Let $A$ be a Cartan matrix of some finite-dimensional simple Lie algebra $g$ and $A^{-1}$ is the inverse matrix. Is it correct that that:
(a) $2 A^{-1}$ is integer-valued matrix only if $g$ is in the …
- 371