Erratums : “Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. <span class="mathjax-formula">$SU(n)$</span> groups”

A NNALES DE L ’I. H. P., SECTION A

W. H. K ^LINK T. T ^ON -T ^HAT

Erratums : “Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. SU (n) groups”

Annales de l’I. H. P., section A, tome 32, n

^o

2 (1980), p. 203

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203.

ERRATUMS

Annales de l’Inst. H.

Poincaré,

Section

A,

^Vol.

XXXI,

^n°

2, 1979,

p. 77-97 et p. 99-113.

Holomorphic

Induction and the Tensor Product

Decomposition

of Irreducible

Representations

of

Compact Groups.

^I.

SU(n) Groups (1)

and

Orthogonal Polynomial

^{Bases for}

Holomorphically

Induced

Representations

^of the General Linear

Groups (2)

Annales de H.

Poincaré,

Section

A,

^Vol.

XXXI,

^nO

2, 1979,

p. 77-97 et p. 99-113.

par W. H. KLINK ^et T. TON-THAT

Ann. Henri Poincare ^, Vol. XXXII, ^n° 2, 1980,

Section A :

Physique ^’ théorique. ^’

1. In

Equations (111-10), (111-12), (111-13)

^and

(111-14)

^{of 1 and}

Equa-

tions

(5), (6)

^and

(9)

^of

2,

^all

pattern

^{addition sums should be}

replaced by general

^{sums over}

primed

variables. For

example, [k’]

⁺

[k"] _ [k]

^should

be

replaced by [k’], [k"],

^{with the sum over all}

possible

^{values of}

[k’],

consistent with the Gelfand ^« betweeness » relations.

Further,

^{in the}

sentence

following Eq. (111-10)

^of

1,

and in the sentence

following Eq. (5)

of

2,

^all reference ^to pattern addition should be deleted.

2. In Lemma 3 of 1 we have

incorrectly

identified the coefficients of

Eq. (111-15)

^{with the}

highest weight

Clebsch-Gordan coefficients. As shown in a

forthcoming

^{article «} Matrix Elements of

GL(n, C)

», the coefficients of

Eq. (111-15)

^{can be used to exhibit}

orthogonal bases,

^and used to compute the actual

highest weight

Clebsch-Gordan coefficients of

Eq. (111-14).