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What is sum of degrees of the irreducible complex characters of the alternating groups?

The background of this question is to calculate the diminsion of a maximal torus of the associated Lie algebra of the group algebra $\mathbb{C} A_n$ for all $n\in \mathbb{N}$.

The corresponding sum for the symmetric group is known by the Frobenius-Schur-Indicators that is to calculate the involutions plus 1 in the symmetric group. This value is also an upper bound for the sum related to the alternating group (see also http://math.stackexchange.com/questions/590402/number-of-involution-in-symmetric-grouphttps://math.stackexchange.com/questions/590402/number-of-involution-in-symmetric-group)

I would like to know the difference betweeen these two values.

In addition the character theory of the alternating groups are closely related to the symmetric group by using Clifford-Theory: some irreducible are still irreducible by restricting them to the alternative group the other ones decompose into two irreducible characters.

In the article http://www.kurims.kyoto-u.ac.jp/EMIS/journals/JACO/Volume5_2/lmm440901p5p3660.fulltext.pdf these two irreducible characters of $A_n$ are investigated based on theorems by Thrall.

What is sum of degrees of the irreducible complex characters of the alternating groups?

The background of this question is to calculate the diminsion of a maximal torus of the associated Lie algebra of the group algebra $\mathbb{C} A_n$ for all $n\in \mathbb{N}$.

The corresponding sum for the symmetric group is known by the Frobenius-Schur-Indicators that is to calculate the involutions plus 1 in the symmetric group. This value is also an upper bound for the sum related to the alternating group (see also http://math.stackexchange.com/questions/590402/number-of-involution-in-symmetric-group)

I would like to know the difference betweeen these two values.

In addition the character theory of the alternating groups are closely related to the symmetric group by using Clifford-Theory: some irreducible are still irreducible by restricting them to the alternative group the other ones decompose into two irreducible characters.

In the article http://www.kurims.kyoto-u.ac.jp/EMIS/journals/JACO/Volume5_2/lmm440901p5p3660.fulltext.pdf these two irreducible characters of $A_n$ are investigated based on theorems by Thrall.

What is sum of degrees of the irreducible complex characters of the alternating groups?

The background of this question is to calculate the diminsion of a maximal torus of the associated Lie algebra of the group algebra $\mathbb{C} A_n$ for all $n\in \mathbb{N}$.

The corresponding sum for the symmetric group is known by the Frobenius-Schur-Indicators that is to calculate the involutions plus 1 in the symmetric group. This value is also an upper bound for the sum related to the alternating group (see also https://math.stackexchange.com/questions/590402/number-of-involution-in-symmetric-group)

I would like to know the difference betweeen these two values.

In addition the character theory of the alternating groups are closely related to the symmetric group by using Clifford-Theory: some irreducible are still irreducible by restricting them to the alternative group the other ones decompose into two irreducible characters.

In the article http://www.kurims.kyoto-u.ac.jp/EMIS/journals/JACO/Volume5_2/lmm440901p5p3660.fulltext.pdf these two irreducible characters of $A_n$ are investigated based on theorems by Thrall.

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Sven Wirsing
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Sum of irreducible complex character degrees for alternating groups

What is sum of degrees of the irreducible complex characters of the alternating groups?

The background of this question is to calculate the diminsion of a maximal torus of the associated Lie algebra of the group algebra $\mathbb{C} A_n$ for all $n\in \mathbb{N}$.

The corresponding sum for the symmetric group is known by the Frobenius-Schur-Indicators that is to calculate the involutions plus 1 in the symmetric group. This value is also an upper bound for the sum related to the alternating group (see also http://math.stackexchange.com/questions/590402/number-of-involution-in-symmetric-group)

I would like to know the difference betweeen these two values.

In addition the character theory of the alternating groups are closely related to the symmetric group by using Clifford-Theory: some irreducible are still irreducible by restricting them to the alternative group the other ones decompose into two irreducible characters.

In the article http://www.kurims.kyoto-u.ac.jp/EMIS/journals/JACO/Volume5_2/lmm440901p5p3660.fulltext.pdf these two irreducible characters of $A_n$ are investigated based on theorems by Thrall.