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YCor
YCor
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Real and Quaternionic Representationsquaternionic representations according to Weightsweights

According to this question, it is easy to know whether a (complex, finite-dimensional) representation is self dual-dual or not: just check if the weight distribution in space is symmetric about the origin.

Now, for self dual-dual representations, we have two possibilities: the representation being real or quaternionic (see this paper).

The The question is: Is it possible to conclude whether the representation is real or quaternionic by seeing the geometric composition of the weights in space, just like the question of self duality?

Any suggestion is welcome.

Is it possible to conclude whether the representation is real or quaternionic by seeing the geometric composition of the weights in space, just like the question of self duality?

Real and Quaternionic Representations according to Weights

According to this question, it is easy to know whether a representation is self dual or not: just check if the weight distribution in space is symmetric about the origin.

Now, for self dual representations, we have two possibilities: the representation being real or quaternionic (see this paper).

The question is: Is it possible to conclude whether the representation is real or quaternionic by seeing the geometric composition of the weights in space, just like the question of self duality?

Any suggestion is welcome.

Real and quaternionic representations according to weights

According to this question, it is easy to know whether a (complex, finite-dimensional) representation is self-dual or not: just check if the weight distribution in space is symmetric about the origin.

Now, for self-dual representations, we have two possibilities: the representation being real or quaternionic (see this paper). The question is:

Is it possible to conclude whether the representation is real or quaternionic by seeing the geometric composition of the weights in space, just like the question of self duality?

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Community Bot
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According to this questionthis question, it is easy to know whether a representation is self dual or not: just check if the weight distribution in space is symmetric about the origin.

Now, for self dual representations, we have two possibilities: the representation being real or quaternionic (see this paper).

The question is: Is it possible to conclude whether the representation is real or quaternionic by seeing the geometric composition of the weights in space, just like the question of self duality?

Any suggestion is welcome.

According to this question, it is easy to know whether a representation is self dual or not: just check if the weight distribution in space is symmetric about the origin.

Now, for self dual representations, we have two possibilities: the representation being real or quaternionic (see this paper).

The question is: Is it possible to conclude whether the representation is real or quaternionic by seeing the geometric composition of the weights in space, just like the question of self duality?

Any suggestion is welcome.

According to this question, it is easy to know whether a representation is self dual or not: just check if the weight distribution in space is symmetric about the origin.

Now, for self dual representations, we have two possibilities: the representation being real or quaternionic (see this paper).

The question is: Is it possible to conclude whether the representation is real or quaternionic by seeing the geometric composition of the weights in space, just like the question of self duality?

Any suggestion is welcome.

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Jjm
Jjm
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Real and Quaternionic Representations according to Weights

According to this question, it is easy to know whether a representation is self dual or not: just check if the weight distribution in space is symmetric about the origin.

Now, for self dual representations, we have two possibilities: the representation being real or quaternionic (see this paper).

The question is: Is it possible to conclude whether the representation is real or quaternionic by seeing the geometric composition of the weights in space, just like the question of self duality?

Any suggestion is welcome.