From 39d58f8555cd9e3905f814cd9b6e453234117fd5 Mon Sep 17 00:00:00 2001 From: Travis Scrimshaw Date: Tue, 18 Apr 2023 13:07:05 +0900 Subject: [PATCH] Fixing a few typos. --- src/sage/algebras/down_up_algebra.py | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/src/sage/algebras/down_up_algebra.py b/src/sage/algebras/down_up_algebra.py index d7371dd6241..4b1a3e0f0b4 100644 --- a/src/sage/algebras/down_up_algebra.py +++ b/src/sage/algebras/down_up_algebra.py @@ -59,7 +59,7 @@ class DownUpAlgebra(CombinatorialFreeModule): where `y` covers `x` and `z` covers `y`. For `r`-differential posets we have `du - ud = r 1` and afford a representation of a :class:`Weyl algebra `. - This is obtained from DU(0, 1, 2r)`. For a `(q,r)`-differential poset, + This is obtained from `DU(0, 1, 2r)`. For a `(q,r)`-differential poset, we have the `d` and `u` operators satisfying .. MATH:: @@ -69,7 +69,8 @@ class DownUpAlgebra(CombinatorialFreeModule): \\ du^2 & = q(q+1) udu - q^3 u^2d + r u, \end{aligned} - or `\alpha = q(q+1)`, `\beta = -q^3`, and `\gamma = r`. + or `\alpha = q(q+1)`, `\beta = -q^3`, and `\gamma = r`. Specializing + `q = -1` recovers the `r`-differential poset relation. EXAMPLES: @@ -478,7 +479,7 @@ class VermaModule(CombinatorialFreeModule): .. MATH:: - d \cdot v_n = \lambda_{n-1} v_{n-1} \qquad\qquad + d \cdot v_n = \lambda_{n-1} v_{n-1}, \qquad\qquad u \cdot v_n = v_{n+1}, where `\lambda_n = \alpha \lambda_{n-1} + \beta \lambda_{n-2} + \gamma`