The following is a list of currently known typos. If you
find more, please tell me, so I can added them to the
list.
Page 28: The third equation from below, after "In the same way".
In the second factor inside the sum in exponent on LHS, the
minus sign should be a plus sign:
x^{\prime}_j -- \frac{1}{jk^j} -->
x^{\prime}_j + \frac{1}{jk^j}
Page 28: The very last equation, there is a missing product
in front of the quotient \frac{q_i - q_\ell}{q_i - p_\ell},
so it should read
\prod_{\ell \in J} \frac{q_i - q_l}{q_i - p_l}
Page 30: Latex mistake on line 12.
A subscript M should be a 'minus sign' (for taking
the pseudo part) followed by the operator M acting
on the exponential (which comes from re-writing the
wave function w as M actong on the exponential).
Page 36: Latex mistake: In Equation (4.10),
if m_i < n < m_i + 1 -->
if m_i < n < m_{i + 1}
Page 38: Line 10 from below: In the definition of F^*,
a |vac> should be < vac| a
Page 39: line 10 from below, indexcharge --> \index(charge)
(just a silly latex typo)
Page 38: line 7 from below, ... < n_2 --> ... < n_s
Page 44: The product in the denominator on RHS of (5.4) is over
all i and j.
Page 44: Remark 5.1, after this, we need only compare degrees -->
after this, we need only compare degrees
and coefficient of leading term.
Page 47: Equation 5.17, u_n --> u
Page 47: Equation 5.17, right hand curly bracket should be left
hand curly bracket and follows = sign.
Page 48: lines 9 and 10 from below,
under the above map (5.17) -->
under the above map (5.15)
Page 50: the definition of \tilde{\del} should end with \cdots
before the RH bracket.
Page 51: top equation: There is a missing ) after \bold{X} in
exponential, and right before the ket |u>
Page 52: In exercise 5.5, exponent of q is ({\ell}^2)/2 rather
than {\ell}/2.
Page 55: Top line of equation (6.6), right hand side, missing
normal ordering of Fermion bilinear inside commutator.
Page 57: In the statement of theorem 6.1, there a linebreak that
shouldn't be there. It's on 2nd line, following "pose".
Page 63: line 10 from below, introduced in Chapter 2 -->
introduced in Chapter 3
very last line, \psi_{-n} \psi^{*}_{n} -->
\psi_{-m} \psi^{*}_{n}
Page 64: 2nd line after equation (7.6):
n \in \Z + 1/2 --> n \in 2 \Z + 1/2, to avoid overlaps.
Next comes the proof of (7.7). One could do it, but only
by taking n \in 2 \Z + 1/2 and shifting the subscripts,
that is by defining
A(t) = \sum_{j \in \Z}
a_{-3/2, 1/2 + 2j} a_{-3/2, 3/2 + 2j}
a_{-1/2, 1/2 + 2j} a_{-1/2, 3/2 + 2j}
t^{j+1}
I had to shift the subscripts to produce \omega(A, B)
without redefining its elements as given in (6.7).
But most importantly, I need the shifts of the 2nd
subscripts of the matrix elements by 2j (rather than j)
to avoid overlaps.
Page 64: second line in Definition 7.1,
by matrices --> by traceless matrices
Page 64: There is a logical jump: Heisenberg algebra is removed
from affine gl_2 to get affine sl_2.
Page 67: On 2nd line of paragraph 4, an algebraic varieties -->
an algebraic variety
Page 70: Dimension of space in which Grassmannian is embedded
is incorrect, there is (-1) inside the binomial factor
that should be outside.
Page 71: of a point Grass(m, V) --> of a point in Grass(m, V)
Page 75: Question 8.2, 2nd line,
det M --> det h
Page 76: The exposition in section 9.1 could be more clear.
Distinguish the various spaces that appear, and
the various algebras. Emphasize that the Grassmannian
is based on W but embedded in F.
Page 77: Equation 9.1, there is a prime on 2nd T on rhs, that
should be on the subscript g.
Page 77: very last line of proof of Theorem 9.1:
A_N --> \cal{A}_N
Page 77: 2nd line after above paragraph:
scalar multiples --> scalar multiple
Page 78: In equation 9.2:
\cal{A} --> \cal{A}_N
Page 80: in first sentence in {\it Proof}, the statment that both
of these operators are annihilation operators is incorrect.
The first is, the second is not.
Page 89: Below equation (10.1), in the equation following "Suppose
that \alpha is written as", there is a missing sign near
the very end
- m_1 - 1, m_1 + 1 --> - m_1 - 1, - m_1 + 1
indicating that the index m_1 is missing.
Page 91: In the expressions for the dual bases:
lhs expression: the \cdots should not be in the denominator.
rhs expression: there should be \cdots at the end.
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